| |
| Autor |
 Zufallsvariable exponentialverteilt |
|
Carly2004
Wenig Aktiv 
Dabei seit: 26.06.2022
Mitteilungen: 37
 |  Themenstart: 2023-06-05
|
Seien ((X_n))_(n\el\ \IN) unabhängige Zufallsvariablen, die jeweils exponentialverteilt mit Parameter \lambda > 0
sind, und S_n = sum(X_k,k=1,n)
Sei außerdem \delta > 0. Finden Sie ein möglichst großes c > 0, sodass für
alle n\el\ \IN gilt:
P(1/n S_n >=(1+\delta)E(X_1))<=e^(-cn)
Ich habe leider keinen Ansatz bzw Idee wie ich vorgehen könnte, kann mir einer ein Tipp geben?
|
 Profil
|
luis52
Senior 
Dabei seit: 24.12.2018
Mitteilungen: 1111
 | Beitrag No.1, eingetragen 2023-06-05
|
\(\begingroup\)\(\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\veps}{\ensuremath{\varepsilon}}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\epsilon}
\newcommand{\veps}{\varepsilon}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
%****************************************************************
%************** Wahrscheinlichkeitsrechnung *********************
%****************************************************************
\newcommand{\dstr}[2]{\ensuremath{\mathcal{#1}(#2)}}
\renewcommand{\dstr}[2]{\ensuremath{\mathtt{#1}(#2)}}
\newcommand{\idd}{\ensuremath{\stackrel{d}{=}}}
\newcommand{\ldd}{\ensuremath{\stackrel{d}{\le}}}
\newcommand{\gdd}{\ensuremath{\stackrel{d}{\ge}}}
\newcommand{\simdot}{\ensuremath{\stackrel{\cdot}{\sim}}}
\newcommand{\asim}{\ensuremath{\stackrel{\,\mathrm{a}}{\sim}}}
\newcommand {\plim}{\ensuremath{\operatorname*{plim}}}
\newcommand{\Pto}{\ensuremath{\stackrel{\textup{P}}{\longrightarrow}}}
\newcommand{\kiw}[2]{#1\ensuremath{\stackrel{\text{P}}{\longrightarrow}}#2}
\newcommand{\Dto}{\ensuremath{\stackrel{\text{D}}{\longrightarrow}}}
\newcommand{\iVto}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\iqmto}{\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}}
\newcommand{\kiqm}[2]{#1\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}#2}
\newcommand{\kiv}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\var}{\operatorname{Var}}
\newcommand{\fVar}{\ensuremath{\mathbf{Var}}}
\newcommand{\fvar}{\ensuremath{\mathbf{Var}}}
\newcommand{\Corr}{\operatorname{Corr}}
\newcommand{\corr}{\operatorname{Corr}}
\newcommand{\cor}{\operatorname{Cor}}
\newcommand{\fCorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fcorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fE}{\ensuremath{\mathbf{E}}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\cov}{\operatorname{Cov}}
\newcommand{\fCov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\fcov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\MSE}{\operatorname{MSE}}
%------------- Fette grosse Buchstaben im Mathemodus -----------
\newcommand{\mbA}{\mathbf{A}}
\newcommand{\mbB}{\mathbf{B}}
\newcommand{\mbC}{\mathbf{C}}
\newcommand{\mbD}{\mathbf{D}}
\newcommand{\mbE}{\mathbf{E}}
\newcommand{\mbF}{\mathbf{F}}
\newcommand{\mbG}{\mathbf{G}}
\newcommand{\mbH}{\mathbf{H}}
\newcommand{\mbI}{\mathbf{I}}
\newcommand{\mbJ}{\mathbf{J}}
\newcommand{\mbK}{\mathbf{K}}
\newcommand{\mbL}{\mathbf{L}}
\newcommand{\mbM}{\mathbf{M}}
\newcommand{\mbN}{\mathbf{N}}
\newcommand{\mbO}{\mathbf{O}}
\newcommand{\mbP}{\mathbf{P}}
\newcommand{\mbQ}{\mathbf{Q}}
\newcommand{\mbR}{\mathbf{R}}
\newcommand{\mbS}{\mathbf{S}}
\newcommand{\mbT}{\mathbf{T}}
\newcommand{\mbU}{\mathbf{U}}
\newcommand{\mbV}{\mathbf{V}}
\newcommand{\mbW}{\mathbf{W}}
\newcommand{\mbX}{\mathbf{X}}
\newcommand{\mbY}{\mathbf{Y}}
\newcommand{\mbZ}{\mathbf{Z}}
%------------- Fette kleine Buchstaben im Mathemodus -----------
\newcommand{\mba}{\mathbf{a}}
\newcommand{\mbb}{\mathbf{b}}
\newcommand{\mbc}{\mathbf{c}}
\newcommand{\mbd}{\mathbf{d}}
\newcommand{\mbe}{\mathbf{e}}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbg}{\mathbf{g}}
\newcommand{\mbh}{\mathbf{h}}
\newcommand{\mbi}{\mathbf{i}}
\newcommand{\mbj}{\mathbf{j}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mbl}{\mathbf{l}}
\newcommand{\mbm}{\mathbf{m}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mbo}{\mathbf{o}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbq}{\mathbf{q}}
\newcommand{\mbr}{\mathbf{r}}
\newcommand{\mbs}{\mathbf{s}}
\newcommand{\mbt}{\mathbf{t}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
%----- Fette Null und fette Eins --------------------------
\newcommand{\fatnull}{\mathbf{0}}
\newcommand{\fateins}{\mathbf{1}}
%----- Fettes Nabla --------------------------
\newcommand{\bnabla}{\boldsymbol{\nabla}}
%----- Fette grosse griechische Buchstaben im Mathemodus -----
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%----- Fette kleine griechische Buchstaben im Mathemodus -----
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\beps}{\boldsymbol{\varepsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\boldeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bvrho}{\boldsymbol{\varrho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bvphi}{\boldsymbol{\varphi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mcA}{\mathcal{A}}
\newcommand{\mcB}{\mathcal{B}}
\newcommand{\mcC}{\mathcal{C}}
\newcommand{\mcD}{\mathcal{D}}
\newcommand{\mcE}{\mathcal{E}}
\newcommand{\mcF}{\mathcal{F}}
\newcommand{\mcG}{\mathcal{G}}
\newcommand{\mcH}{\mathcal{H}}
\newcommand{\mcI}{\mathcal{I}}
\newcommand{\mcJ}{\mathcal{J}}
\newcommand{\mcK}{\mathcal{K}}
\newcommand{\mcL}{\mathcal{L}}
\newcommand{\mcM}{\mathcal{M}}
\newcommand{\mcN}{\mathcal{N}}
\newcommand{\mcO}{\mathcal{O}}
\newcommand{\mcP}{\mathcal{P}}
\newcommand{\mcQ}{\mathcal{Q}}
\newcommand{\mcR}{\mathcal{R}}
\newcommand{\mcS}{\mathcal{S}}
\newcommand{\mcT}{\mathcal{T}}
\newcommand{\mcU}{\mathcal{U}}
\newcommand{\mcV}{\mathcal{V}}
\newcommand{\mcW}{\mathcal{W}}
\newcommand{\mcX}{\mathcal{X}}
\newcommand{\mcY}{\mathcal{Y}}
\newcommand{\mcZ}{\mathcal{Z}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mca}{\mathcal{A}}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcd}{\mathcal{D}}
\newcommand{\mce}{\mathcal{E}}
\newcommand{\mcf}{\mathcal{F}}
\newcommand{\mcg}{\mathcal{G}}
\newcommand{\mch}{\mathcal{H}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mcj}{\mathcal{J}}
\newcommand{\mck}{\mathcal{K}}
\newcommand{\mcl}{\mathcal{L}}
\newcommand{\mcm}{\mathcal{M}}
\newcommand{\mcn}{\mathcal{N}}
\newcommand{\mco}{\mathcal{O}}
\newcommand{\mcp}{\mathcal{P}}
\newcommand{\mcq}{\mathcal{Q}}
\newcommand{\mcr}{\mathcal{R}}
\newcommand{\mcs}{\mathcal{S}}
\newcommand{\mct}{\mathcal{T}}
\newcommand{\mcu}{\mathcal{U}}
\newcommand{\mcv}{\mathcal{V}}
\newcommand{\mcw}{\mathcal{W}}
\newcommand{\mcx}{\mathcal{X}}
\newcommand{\mcy}{\mathcal{Y}}
\newcommand{\mcz}{\mathcal{Z}}
%---------- Doppelsumme ------------------------------------------
\newcommand{\dblsum}[1]{\ensuremath{\mathop{\sum\sum}\limits_{#1}}}
%---------- \argmin und \argmax ------------------------------
\newcommand{\argmin}{\ensuremath{\operatorname*{arg{}min}}}
\newcommand{\argmax}{\ensuremath{\operatorname*{arg{}max}}}
%---------- Folgen ------------------------------------------
\newcommand{\avec}[2]{#1_1,\ldots,#1_{#2}}
\newcommand{\avecc}[2]{\ensuremath{#1_1,#1_2,\ldots,#1_{#2}}}
\newcommand{\aveccc}[3]{\ensuremath{(#1_{#2},\ldots,#1_{#3})}}
%---------- Geordnete Werte ---------------------------------------
\newcommand{\ord}[2]{\ensuremath{#1_{(1)},\ldots,#1_{(#2)}}}
\newcommand{\ordd}[2]{\ensuremath{#1_{(1)}\le#1_{(2)}\le\cdots\le#1_{(#2)}}}
\newcommand{\ordstat}[2]{\ensuremath{#1_{(#2)}}}
\newcommand{\ordne}[3]{\ensuremath{#1_{(1)}#3 #1_{(2)}#3\dots#3#1_{(#2)}}}
\)
\quoteon(2023-06-05 03:50 - Carly2004 im Themenstart)
kann mir einer ein Tipp geben?
\quoteoff
$S_n$ ist Erlang-verteilt.\(\endgroup\)
|
Profil
|
Carly2004
Wenig Aktiv
Dabei seit: 26.06.2022
Mitteilungen: 37
| Beitrag No.2, vom Themenstarter, eingetragen 2023-06-05
|
Ich kann damit leider immernoch nicht viel Anfangen. :(
|
Profil
|
luis52
Senior
Dabei seit: 24.12.2018
Mitteilungen: 1111
| Beitrag No.3, eingetragen 2023-06-05
|
\(\begingroup\)\(\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\veps}{\ensuremath{\varepsilon}}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\epsilon}
\newcommand{\veps}{\varepsilon}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
%****************************************************************
%************** Wahrscheinlichkeitsrechnung *********************
%****************************************************************
\newcommand{\dstr}[2]{\ensuremath{\mathcal{#1}(#2)}}
\renewcommand{\dstr}[2]{\ensuremath{\mathtt{#1}(#2)}}
\newcommand{\idd}{\ensuremath{\stackrel{d}{=}}}
\newcommand{\ldd}{\ensuremath{\stackrel{d}{\le}}}
\newcommand{\gdd}{\ensuremath{\stackrel{d}{\ge}}}
\newcommand{\simdot}{\ensuremath{\stackrel{\cdot}{\sim}}}
\newcommand{\asim}{\ensuremath{\stackrel{\,\mathrm{a}}{\sim}}}
\newcommand {\plim}{\ensuremath{\operatorname*{plim}}}
\newcommand{\Pto}{\ensuremath{\stackrel{\textup{P}}{\longrightarrow}}}
\newcommand{\kiw}[2]{#1\ensuremath{\stackrel{\text{P}}{\longrightarrow}}#2}
\newcommand{\Dto}{\ensuremath{\stackrel{\text{D}}{\longrightarrow}}}
\newcommand{\iVto}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\iqmto}{\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}}
\newcommand{\kiqm}[2]{#1\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}#2}
\newcommand{\kiv}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\var}{\operatorname{Var}}
\newcommand{\fVar}{\ensuremath{\mathbf{Var}}}
\newcommand{\fvar}{\ensuremath{\mathbf{Var}}}
\newcommand{\Corr}{\operatorname{Corr}}
\newcommand{\corr}{\operatorname{Corr}}
\newcommand{\cor}{\operatorname{Cor}}
\newcommand{\fCorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fcorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fE}{\ensuremath{\mathbf{E}}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\cov}{\operatorname{Cov}}
\newcommand{\fCov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\fcov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\MSE}{\operatorname{MSE}}
%------------- Fette grosse Buchstaben im Mathemodus -----------
\newcommand{\mbA}{\mathbf{A}}
\newcommand{\mbB}{\mathbf{B}}
\newcommand{\mbC}{\mathbf{C}}
\newcommand{\mbD}{\mathbf{D}}
\newcommand{\mbE}{\mathbf{E}}
\newcommand{\mbF}{\mathbf{F}}
\newcommand{\mbG}{\mathbf{G}}
\newcommand{\mbH}{\mathbf{H}}
\newcommand{\mbI}{\mathbf{I}}
\newcommand{\mbJ}{\mathbf{J}}
\newcommand{\mbK}{\mathbf{K}}
\newcommand{\mbL}{\mathbf{L}}
\newcommand{\mbM}{\mathbf{M}}
\newcommand{\mbN}{\mathbf{N}}
\newcommand{\mbO}{\mathbf{O}}
\newcommand{\mbP}{\mathbf{P}}
\newcommand{\mbQ}{\mathbf{Q}}
\newcommand{\mbR}{\mathbf{R}}
\newcommand{\mbS}{\mathbf{S}}
\newcommand{\mbT}{\mathbf{T}}
\newcommand{\mbU}{\mathbf{U}}
\newcommand{\mbV}{\mathbf{V}}
\newcommand{\mbW}{\mathbf{W}}
\newcommand{\mbX}{\mathbf{X}}
\newcommand{\mbY}{\mathbf{Y}}
\newcommand{\mbZ}{\mathbf{Z}}
%------------- Fette kleine Buchstaben im Mathemodus -----------
\newcommand{\mba}{\mathbf{a}}
\newcommand{\mbb}{\mathbf{b}}
\newcommand{\mbc}{\mathbf{c}}
\newcommand{\mbd}{\mathbf{d}}
\newcommand{\mbe}{\mathbf{e}}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbg}{\mathbf{g}}
\newcommand{\mbh}{\mathbf{h}}
\newcommand{\mbi}{\mathbf{i}}
\newcommand{\mbj}{\mathbf{j}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mbl}{\mathbf{l}}
\newcommand{\mbm}{\mathbf{m}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mbo}{\mathbf{o}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbq}{\mathbf{q}}
\newcommand{\mbr}{\mathbf{r}}
\newcommand{\mbs}{\mathbf{s}}
\newcommand{\mbt}{\mathbf{t}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
%----- Fette Null und fette Eins --------------------------
\newcommand{\fatnull}{\mathbf{0}}
\newcommand{\fateins}{\mathbf{1}}
%----- Fettes Nabla --------------------------
\newcommand{\bnabla}{\boldsymbol{\nabla}}
%----- Fette grosse griechische Buchstaben im Mathemodus -----
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%----- Fette kleine griechische Buchstaben im Mathemodus -----
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\beps}{\boldsymbol{\varepsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\boldeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bvrho}{\boldsymbol{\varrho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bvphi}{\boldsymbol{\varphi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mcA}{\mathcal{A}}
\newcommand{\mcB}{\mathcal{B}}
\newcommand{\mcC}{\mathcal{C}}
\newcommand{\mcD}{\mathcal{D}}
\newcommand{\mcE}{\mathcal{E}}
\newcommand{\mcF}{\mathcal{F}}
\newcommand{\mcG}{\mathcal{G}}
\newcommand{\mcH}{\mathcal{H}}
\newcommand{\mcI}{\mathcal{I}}
\newcommand{\mcJ}{\mathcal{J}}
\newcommand{\mcK}{\mathcal{K}}
\newcommand{\mcL}{\mathcal{L}}
\newcommand{\mcM}{\mathcal{M}}
\newcommand{\mcN}{\mathcal{N}}
\newcommand{\mcO}{\mathcal{O}}
\newcommand{\mcP}{\mathcal{P}}
\newcommand{\mcQ}{\mathcal{Q}}
\newcommand{\mcR}{\mathcal{R}}
\newcommand{\mcS}{\mathcal{S}}
\newcommand{\mcT}{\mathcal{T}}
\newcommand{\mcU}{\mathcal{U}}
\newcommand{\mcV}{\mathcal{V}}
\newcommand{\mcW}{\mathcal{W}}
\newcommand{\mcX}{\mathcal{X}}
\newcommand{\mcY}{\mathcal{Y}}
\newcommand{\mcZ}{\mathcal{Z}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mca}{\mathcal{A}}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcd}{\mathcal{D}}
\newcommand{\mce}{\mathcal{E}}
\newcommand{\mcf}{\mathcal{F}}
\newcommand{\mcg}{\mathcal{G}}
\newcommand{\mch}{\mathcal{H}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mcj}{\mathcal{J}}
\newcommand{\mck}{\mathcal{K}}
\newcommand{\mcl}{\mathcal{L}}
\newcommand{\mcm}{\mathcal{M}}
\newcommand{\mcn}{\mathcal{N}}
\newcommand{\mco}{\mathcal{O}}
\newcommand{\mcp}{\mathcal{P}}
\newcommand{\mcq}{\mathcal{Q}}
\newcommand{\mcr}{\mathcal{R}}
\newcommand{\mcs}{\mathcal{S}}
\newcommand{\mct}{\mathcal{T}}
\newcommand{\mcu}{\mathcal{U}}
\newcommand{\mcv}{\mathcal{V}}
\newcommand{\mcw}{\mathcal{W}}
\newcommand{\mcx}{\mathcal{X}}
\newcommand{\mcy}{\mathcal{Y}}
\newcommand{\mcz}{\mathcal{Z}}
%---------- Doppelsumme ------------------------------------------
\newcommand{\dblsum}[1]{\ensuremath{\mathop{\sum\sum}\limits_{#1}}}
%---------- \argmin und \argmax ------------------------------
\newcommand{\argmin}{\ensuremath{\operatorname*{arg{}min}}}
\newcommand{\argmax}{\ensuremath{\operatorname*{arg{}max}}}
%---------- Folgen ------------------------------------------
\newcommand{\avec}[2]{#1_1,\ldots,#1_{#2}}
\newcommand{\avecc}[2]{\ensuremath{#1_1,#1_2,\ldots,#1_{#2}}}
\newcommand{\aveccc}[3]{\ensuremath{(#1_{#2},\ldots,#1_{#3})}}
%---------- Geordnete Werte ---------------------------------------
\newcommand{\ord}[2]{\ensuremath{#1_{(1)},\ldots,#1_{(#2)}}}
\newcommand{\ordd}[2]{\ensuremath{#1_{(1)}\le#1_{(2)}\le\cdots\le#1_{(#2)}}}
\newcommand{\ordstat}[2]{\ensuremath{#1_{(#2)}}}
\newcommand{\ordne}[3]{\ensuremath{#1_{(1)}#3 #1_{(2)}#3\dots#3#1_{(#2)}}}
\)
\quoteon(2023-06-05 15:09 - Carly2004 in Beitrag No. 2)
Ich kann damit leider immernoch nicht viel Anfangen. :(
\quoteoff
Die Verteilungsfunktion ist damit
\[P(S_n\le x)=1-\sum_{j=0}^{n-1}\frac{(\lambda x)^j}{j!}e^{-\lambda x}\,,\quad x>0\,.\]
\(\endgroup\)
|
Profil
|
luis52
Senior 
Dabei seit: 24.12.2018
Mitteilungen: 1111
| Beitrag No.4, eingetragen 2023-06-06
|
Vielleicht kommt man auch alternativ mit der Markowschen Ungleichung weiter.
|
Profil
|
Carly2004
Wenig Aktiv 
Dabei seit: 26.06.2022
Mitteilungen: 37
| Beitrag No.5, vom Themenstarter, eingetragen 2023-06-08
|
Also ich ahbe es durchgerechnet, ich habe als Ergebnis:
c=-log(1+\delta)-\lambda+1+\delta
Kann das so stimmen
|
Profil
|
luis52
Senior
Dabei seit: 24.12.2018
Mitteilungen: 1111
| Beitrag No.6, eingetragen 2023-06-08
|
\(\begingroup\)\(\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\veps}{\ensuremath{\varepsilon}}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\epsilon}
\newcommand{\veps}{\varepsilon}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
%****************************************************************
%************** Wahrscheinlichkeitsrechnung *********************
%****************************************************************
\newcommand{\dstr}[2]{\ensuremath{\mathcal{#1}(#2)}}
\renewcommand{\dstr}[2]{\ensuremath{\mathtt{#1}(#2)}}
\newcommand{\idd}{\ensuremath{\stackrel{d}{=}}}
\newcommand{\ldd}{\ensuremath{\stackrel{d}{\le}}}
\newcommand{\gdd}{\ensuremath{\stackrel{d}{\ge}}}
\newcommand{\simdot}{\ensuremath{\stackrel{\cdot}{\sim}}}
\newcommand{\asim}{\ensuremath{\stackrel{\,\mathrm{a}}{\sim}}}
\newcommand {\plim}{\ensuremath{\operatorname*{plim}}}
\newcommand{\Pto}{\ensuremath{\stackrel{\textup{P}}{\longrightarrow}}}
\newcommand{\kiw}[2]{#1\ensuremath{\stackrel{\text{P}}{\longrightarrow}}#2}
\newcommand{\Dto}{\ensuremath{\stackrel{\text{D}}{\longrightarrow}}}
\newcommand{\iVto}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\iqmto}{\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}}
\newcommand{\kiqm}[2]{#1\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}#2}
\newcommand{\kiv}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\var}{\operatorname{Var}}
\newcommand{\fVar}{\ensuremath{\mathbf{Var}}}
\newcommand{\fvar}{\ensuremath{\mathbf{Var}}}
\newcommand{\Corr}{\operatorname{Corr}}
\newcommand{\corr}{\operatorname{Corr}}
\newcommand{\cor}{\operatorname{Cor}}
\newcommand{\fCorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fcorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fE}{\ensuremath{\mathbf{E}}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\cov}{\operatorname{Cov}}
\newcommand{\fCov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\fcov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\MSE}{\operatorname{MSE}}
%------------- Fette grosse Buchstaben im Mathemodus -----------
\newcommand{\mbA}{\mathbf{A}}
\newcommand{\mbB}{\mathbf{B}}
\newcommand{\mbC}{\mathbf{C}}
\newcommand{\mbD}{\mathbf{D}}
\newcommand{\mbE}{\mathbf{E}}
\newcommand{\mbF}{\mathbf{F}}
\newcommand{\mbG}{\mathbf{G}}
\newcommand{\mbH}{\mathbf{H}}
\newcommand{\mbI}{\mathbf{I}}
\newcommand{\mbJ}{\mathbf{J}}
\newcommand{\mbK}{\mathbf{K}}
\newcommand{\mbL}{\mathbf{L}}
\newcommand{\mbM}{\mathbf{M}}
\newcommand{\mbN}{\mathbf{N}}
\newcommand{\mbO}{\mathbf{O}}
\newcommand{\mbP}{\mathbf{P}}
\newcommand{\mbQ}{\mathbf{Q}}
\newcommand{\mbR}{\mathbf{R}}
\newcommand{\mbS}{\mathbf{S}}
\newcommand{\mbT}{\mathbf{T}}
\newcommand{\mbU}{\mathbf{U}}
\newcommand{\mbV}{\mathbf{V}}
\newcommand{\mbW}{\mathbf{W}}
\newcommand{\mbX}{\mathbf{X}}
\newcommand{\mbY}{\mathbf{Y}}
\newcommand{\mbZ}{\mathbf{Z}}
%------------- Fette kleine Buchstaben im Mathemodus -----------
\newcommand{\mba}{\mathbf{a}}
\newcommand{\mbb}{\mathbf{b}}
\newcommand{\mbc}{\mathbf{c}}
\newcommand{\mbd}{\mathbf{d}}
\newcommand{\mbe}{\mathbf{e}}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbg}{\mathbf{g}}
\newcommand{\mbh}{\mathbf{h}}
\newcommand{\mbi}{\mathbf{i}}
\newcommand{\mbj}{\mathbf{j}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mbl}{\mathbf{l}}
\newcommand{\mbm}{\mathbf{m}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mbo}{\mathbf{o}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbq}{\mathbf{q}}
\newcommand{\mbr}{\mathbf{r}}
\newcommand{\mbs}{\mathbf{s}}
\newcommand{\mbt}{\mathbf{t}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
%----- Fette Null und fette Eins --------------------------
\newcommand{\fatnull}{\mathbf{0}}
\newcommand{\fateins}{\mathbf{1}}
%----- Fettes Nabla --------------------------
\newcommand{\bnabla}{\boldsymbol{\nabla}}
%----- Fette grosse griechische Buchstaben im Mathemodus -----
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%----- Fette kleine griechische Buchstaben im Mathemodus -----
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\beps}{\boldsymbol{\varepsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\boldeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bvrho}{\boldsymbol{\varrho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bvphi}{\boldsymbol{\varphi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mcA}{\mathcal{A}}
\newcommand{\mcB}{\mathcal{B}}
\newcommand{\mcC}{\mathcal{C}}
\newcommand{\mcD}{\mathcal{D}}
\newcommand{\mcE}{\mathcal{E}}
\newcommand{\mcF}{\mathcal{F}}
\newcommand{\mcG}{\mathcal{G}}
\newcommand{\mcH}{\mathcal{H}}
\newcommand{\mcI}{\mathcal{I}}
\newcommand{\mcJ}{\mathcal{J}}
\newcommand{\mcK}{\mathcal{K}}
\newcommand{\mcL}{\mathcal{L}}
\newcommand{\mcM}{\mathcal{M}}
\newcommand{\mcN}{\mathcal{N}}
\newcommand{\mcO}{\mathcal{O}}
\newcommand{\mcP}{\mathcal{P}}
\newcommand{\mcQ}{\mathcal{Q}}
\newcommand{\mcR}{\mathcal{R}}
\newcommand{\mcS}{\mathcal{S}}
\newcommand{\mcT}{\mathcal{T}}
\newcommand{\mcU}{\mathcal{U}}
\newcommand{\mcV}{\mathcal{V}}
\newcommand{\mcW}{\mathcal{W}}
\newcommand{\mcX}{\mathcal{X}}
\newcommand{\mcY}{\mathcal{Y}}
\newcommand{\mcZ}{\mathcal{Z}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mca}{\mathcal{A}}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcd}{\mathcal{D}}
\newcommand{\mce}{\mathcal{E}}
\newcommand{\mcf}{\mathcal{F}}
\newcommand{\mcg}{\mathcal{G}}
\newcommand{\mch}{\mathcal{H}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mcj}{\mathcal{J}}
\newcommand{\mck}{\mathcal{K}}
\newcommand{\mcl}{\mathcal{L}}
\newcommand{\mcm}{\mathcal{M}}
\newcommand{\mcn}{\mathcal{N}}
\newcommand{\mco}{\mathcal{O}}
\newcommand{\mcp}{\mathcal{P}}
\newcommand{\mcq}{\mathcal{Q}}
\newcommand{\mcr}{\mathcal{R}}
\newcommand{\mcs}{\mathcal{S}}
\newcommand{\mct}{\mathcal{T}}
\newcommand{\mcu}{\mathcal{U}}
\newcommand{\mcv}{\mathcal{V}}
\newcommand{\mcw}{\mathcal{W}}
\newcommand{\mcx}{\mathcal{X}}
\newcommand{\mcy}{\mathcal{Y}}
\newcommand{\mcz}{\mathcal{Z}}
%---------- Doppelsumme ------------------------------------------
\newcommand{\dblsum}[1]{\ensuremath{\mathop{\sum\sum}\limits_{#1}}}
%---------- \argmin und \argmax ------------------------------
\newcommand{\argmin}{\ensuremath{\operatorname*{arg{}min}}}
\newcommand{\argmax}{\ensuremath{\operatorname*{arg{}max}}}
%---------- Folgen ------------------------------------------
\newcommand{\avec}[2]{#1_1,\ldots,#1_{#2}}
\newcommand{\avecc}[2]{\ensuremath{#1_1,#1_2,\ldots,#1_{#2}}}
\newcommand{\aveccc}[3]{\ensuremath{(#1_{#2},\ldots,#1_{#3})}}
%---------- Geordnete Werte ---------------------------------------
\newcommand{\ord}[2]{\ensuremath{#1_{(1)},\ldots,#1_{(#2)}}}
\newcommand{\ordd}[2]{\ensuremath{#1_{(1)}\le#1_{(2)}\le\cdots\le#1_{(#2)}}}
\newcommand{\ordstat}[2]{\ensuremath{#1_{(#2)}}}
\newcommand{\ordne}[3]{\ensuremath{#1_{(1)}#3 #1_{(2)}#3\dots#3#1_{(#2)}}}
\)
\quoteon(2023-06-08 17:03 - Carly2004 in Beitrag No. 5)
Also ich ahbe es durchgerechnet, ich habe als Ergebnis:
c=-log(1+\delta)-\lambda+1+\delta
Kann das so stimmen
\quoteoff
Hm, "deine" obere Schranke lautet also
\[\exp(-cn)=\exp(-(-\log(1+\delta)-\lambda+1+\delta)n))\,,\]
korrekt?
Fuer $n=2$, $\lambda=2$ und $\delta=1$ erhaelt man so:
\sourceon R
R> n <-2
R> lambda <- 2
R> delta <-1
R> exp(-(-log(1+delta)-lambda+1+delta)*n)
[1] 4
\sourceoff
Arg konservativ, findest du nicht?
Wie waere es, wenn du deine Herleitung mal vorstellst?
\(\endgroup\)
|
Profil
|
Carly2004
Wenig Aktiv
Dabei seit: 26.06.2022
Mitteilungen: 37
| Beitrag No.7, vom Themenstarter, eingetragen 2023-06-09
|
Ok.
P(1/n*S_n>=(1+\delta)E(X_1))
=P(S_n>=n*(1+\delta)E(X_1))
<=exp[-tn(1+\delta)E(X_1)]E(exp[t*S_n])
=exp[-tn(1+\delta)E(X_1)]M_(X1)^n
=exp[n(logM_(X1)(t))-t(1+\delta)E(X_1))]
Minimiere g(t)=logM_(X1)(t))-t(1+\delta)E(X_1))=log(\lambda/(\lambda-t))-t(1+\delta)1/\lambda
Da habe ich heraus t=\lambda-\lambda^2/(1+\delta)<\lambda (muss wegen M_(X1) gelten)
Dann habe ich das t eingesetzt:
=exp[n(log(\lambda/(\lambda+\lambda^2/(1+\delta)-\lambda)+(\lambda^2/(1+\delta)-\lambda)(1+\delta)1/\lambda)]
=exp[n*log(1+\delta)+\lambda-(1+\delta))]
=exp[-(-log(1+\delta)-\lambda+(1+\delta))n]
=>c=-log(1+\delta)-\lambda+(1+\delta)
|
Profil
|
luis52
Senior
Dabei seit: 24.12.2018
Mitteilungen: 1111
| Beitrag No.8, eingetragen 2023-06-09
|
\(\begingroup\)\(\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\veps}{\ensuremath{\varepsilon}}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\epsilon}
\newcommand{\veps}{\varepsilon}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
%****************************************************************
%************** Wahrscheinlichkeitsrechnung *********************
%****************************************************************
\newcommand{\dstr}[2]{\ensuremath{\mathcal{#1}(#2)}}
\renewcommand{\dstr}[2]{\ensuremath{\mathtt{#1}(#2)}}
\newcommand{\idd}{\ensuremath{\stackrel{d}{=}}}
\newcommand{\ldd}{\ensuremath{\stackrel{d}{\le}}}
\newcommand{\gdd}{\ensuremath{\stackrel{d}{\ge}}}
\newcommand{\simdot}{\ensuremath{\stackrel{\cdot}{\sim}}}
\newcommand{\asim}{\ensuremath{\stackrel{\,\mathrm{a}}{\sim}}}
\newcommand {\plim}{\ensuremath{\operatorname*{plim}}}
\newcommand{\Pto}{\ensuremath{\stackrel{\textup{P}}{\longrightarrow}}}
\newcommand{\kiw}[2]{#1\ensuremath{\stackrel{\text{P}}{\longrightarrow}}#2}
\newcommand{\Dto}{\ensuremath{\stackrel{\text{D}}{\longrightarrow}}}
\newcommand{\iVto}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\iqmto}{\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}}
\newcommand{\kiqm}[2]{#1\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}#2}
\newcommand{\kiv}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\var}{\operatorname{Var}}
\newcommand{\fVar}{\ensuremath{\mathbf{Var}}}
\newcommand{\fvar}{\ensuremath{\mathbf{Var}}}
\newcommand{\Corr}{\operatorname{Corr}}
\newcommand{\corr}{\operatorname{Corr}}
\newcommand{\cor}{\operatorname{Cor}}
\newcommand{\fCorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fcorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fE}{\ensuremath{\mathbf{E}}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\cov}{\operatorname{Cov}}
\newcommand{\fCov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\fcov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\MSE}{\operatorname{MSE}}
%------------- Fette grosse Buchstaben im Mathemodus -----------
\newcommand{\mbA}{\mathbf{A}}
\newcommand{\mbB}{\mathbf{B}}
\newcommand{\mbC}{\mathbf{C}}
\newcommand{\mbD}{\mathbf{D}}
\newcommand{\mbE}{\mathbf{E}}
\newcommand{\mbF}{\mathbf{F}}
\newcommand{\mbG}{\mathbf{G}}
\newcommand{\mbH}{\mathbf{H}}
\newcommand{\mbI}{\mathbf{I}}
\newcommand{\mbJ}{\mathbf{J}}
\newcommand{\mbK}{\mathbf{K}}
\newcommand{\mbL}{\mathbf{L}}
\newcommand{\mbM}{\mathbf{M}}
\newcommand{\mbN}{\mathbf{N}}
\newcommand{\mbO}{\mathbf{O}}
\newcommand{\mbP}{\mathbf{P}}
\newcommand{\mbQ}{\mathbf{Q}}
\newcommand{\mbR}{\mathbf{R}}
\newcommand{\mbS}{\mathbf{S}}
\newcommand{\mbT}{\mathbf{T}}
\newcommand{\mbU}{\mathbf{U}}
\newcommand{\mbV}{\mathbf{V}}
\newcommand{\mbW}{\mathbf{W}}
\newcommand{\mbX}{\mathbf{X}}
\newcommand{\mbY}{\mathbf{Y}}
\newcommand{\mbZ}{\mathbf{Z}}
%------------- Fette kleine Buchstaben im Mathemodus -----------
\newcommand{\mba}{\mathbf{a}}
\newcommand{\mbb}{\mathbf{b}}
\newcommand{\mbc}{\mathbf{c}}
\newcommand{\mbd}{\mathbf{d}}
\newcommand{\mbe}{\mathbf{e}}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbg}{\mathbf{g}}
\newcommand{\mbh}{\mathbf{h}}
\newcommand{\mbi}{\mathbf{i}}
\newcommand{\mbj}{\mathbf{j}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mbl}{\mathbf{l}}
\newcommand{\mbm}{\mathbf{m}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mbo}{\mathbf{o}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbq}{\mathbf{q}}
\newcommand{\mbr}{\mathbf{r}}
\newcommand{\mbs}{\mathbf{s}}
\newcommand{\mbt}{\mathbf{t}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
%----- Fette Null und fette Eins --------------------------
\newcommand{\fatnull}{\mathbf{0}}
\newcommand{\fateins}{\mathbf{1}}
%----- Fettes Nabla --------------------------
\newcommand{\bnabla}{\boldsymbol{\nabla}}
%----- Fette grosse griechische Buchstaben im Mathemodus -----
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%----- Fette kleine griechische Buchstaben im Mathemodus -----
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\beps}{\boldsymbol{\varepsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\boldeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bvrho}{\boldsymbol{\varrho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bvphi}{\boldsymbol{\varphi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mcA}{\mathcal{A}}
\newcommand{\mcB}{\mathcal{B}}
\newcommand{\mcC}{\mathcal{C}}
\newcommand{\mcD}{\mathcal{D}}
\newcommand{\mcE}{\mathcal{E}}
\newcommand{\mcF}{\mathcal{F}}
\newcommand{\mcG}{\mathcal{G}}
\newcommand{\mcH}{\mathcal{H}}
\newcommand{\mcI}{\mathcal{I}}
\newcommand{\mcJ}{\mathcal{J}}
\newcommand{\mcK}{\mathcal{K}}
\newcommand{\mcL}{\mathcal{L}}
\newcommand{\mcM}{\mathcal{M}}
\newcommand{\mcN}{\mathcal{N}}
\newcommand{\mcO}{\mathcal{O}}
\newcommand{\mcP}{\mathcal{P}}
\newcommand{\mcQ}{\mathcal{Q}}
\newcommand{\mcR}{\mathcal{R}}
\newcommand{\mcS}{\mathcal{S}}
\newcommand{\mcT}{\mathcal{T}}
\newcommand{\mcU}{\mathcal{U}}
\newcommand{\mcV}{\mathcal{V}}
\newcommand{\mcW}{\mathcal{W}}
\newcommand{\mcX}{\mathcal{X}}
\newcommand{\mcY}{\mathcal{Y}}
\newcommand{\mcZ}{\mathcal{Z}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mca}{\mathcal{A}}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcd}{\mathcal{D}}
\newcommand{\mce}{\mathcal{E}}
\newcommand{\mcf}{\mathcal{F}}
\newcommand{\mcg}{\mathcal{G}}
\newcommand{\mch}{\mathcal{H}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mcj}{\mathcal{J}}
\newcommand{\mck}{\mathcal{K}}
\newcommand{\mcl}{\mathcal{L}}
\newcommand{\mcm}{\mathcal{M}}
\newcommand{\mcn}{\mathcal{N}}
\newcommand{\mco}{\mathcal{O}}
\newcommand{\mcp}{\mathcal{P}}
\newcommand{\mcq}{\mathcal{Q}}
\newcommand{\mcr}{\mathcal{R}}
\newcommand{\mcs}{\mathcal{S}}
\newcommand{\mct}{\mathcal{T}}
\newcommand{\mcu}{\mathcal{U}}
\newcommand{\mcv}{\mathcal{V}}
\newcommand{\mcw}{\mathcal{W}}
\newcommand{\mcx}{\mathcal{X}}
\newcommand{\mcy}{\mathcal{Y}}
\newcommand{\mcz}{\mathcal{Z}}
%---------- Doppelsumme ------------------------------------------
\newcommand{\dblsum}[1]{\ensuremath{\mathop{\sum\sum}\limits_{#1}}}
%---------- \argmin und \argmax ------------------------------
\newcommand{\argmin}{\ensuremath{\operatorname*{arg{}min}}}
\newcommand{\argmax}{\ensuremath{\operatorname*{arg{}max}}}
%---------- Folgen ------------------------------------------
\newcommand{\avec}[2]{#1_1,\ldots,#1_{#2}}
\newcommand{\avecc}[2]{\ensuremath{#1_1,#1_2,\ldots,#1_{#2}}}
\newcommand{\aveccc}[3]{\ensuremath{(#1_{#2},\ldots,#1_{#3})}}
%---------- Geordnete Werte ---------------------------------------
\newcommand{\ord}[2]{\ensuremath{#1_{(1)},\ldots,#1_{(#2)}}}
\newcommand{\ordd}[2]{\ensuremath{#1_{(1)}\le#1_{(2)}\le\cdots\le#1_{(#2)}}}
\newcommand{\ordstat}[2]{\ensuremath{#1_{(#2)}}}
\newcommand{\ordne}[3]{\ensuremath{#1_{(1)}#3 #1_{(2)}#3\dots#3#1_{(#2)}}}
\)
Die erste Ungleichung
\[P(S_n\ge n(1+\delta)\E(X_1))\le
\exp[-tn(1+\delta)\E(X_1)]\E(\exp[tS_n])\]
verstehe ich ueberhaupt nicht. Wo kommt sie her? Was ist $t$? Uebrigens $\E(X_1)=1/\lambda$ ... \(\endgroup\)
|
Profil
|
Carly2004
Wenig Aktiv
Dabei seit: 26.06.2022
Mitteilungen: 37
| Beitrag No.9, vom Themenstarter, eingetragen 2023-06-09
|
Aus der Markov-Ungleichung mit
f(x)=e^tx mit t>0
|
Profil
|
luis52
Senior
Dabei seit: 24.12.2018
Mitteilungen: 1111
| Beitrag No.10, eingetragen 2023-06-09
|
\(\begingroup\)\(\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\veps}{\ensuremath{\varepsilon}}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
\newcommand{\diag}{\operatorname{diag}} % diag
\newcommand{\Diag}{\operatorname{Diag}} % Diag
\newcommand{\tr}{\operatorname{tr}} % Spur
\newcommand{\rg}{\operatorname{rg}} % Rang
\newcommand{\logit}{\operatorname{logit}} % logit
\newcommand{\sign}{\operatorname{sign}} % logit
\newcommand{\AR}{\operatorname{AR}} % AR-Prozess
\newcommand{\MA}{\operatorname{MA}} % MA-Prozess
\newcommand{\ARMA}{\operatorname{ARMA}} % ARMA-Prozess
\newcommand{\VAR}{\operatorname{VAR}} % VAR-Prozess
\newcommand{\spn}{\operatorname{span}} % span
%****************************************************************
%************************** Abkuerzungen ************************
%****************************************************************
\newcommand{\eps}{\epsilon}
\newcommand{\veps}{\varepsilon}
%****************************************************************
%************************** Miszellanien ************************
%****************************************************************
\newcommand{\mlink}[1]{\qquad\text{#1}\qquad}
%****************************************************************
%************** Wahrscheinlichkeitsrechnung *********************
%****************************************************************
\newcommand{\dstr}[2]{\ensuremath{\mathcal{#1}(#2)}}
\renewcommand{\dstr}[2]{\ensuremath{\mathtt{#1}(#2)}}
\newcommand{\idd}{\ensuremath{\stackrel{d}{=}}}
\newcommand{\ldd}{\ensuremath{\stackrel{d}{\le}}}
\newcommand{\gdd}{\ensuremath{\stackrel{d}{\ge}}}
\newcommand{\simdot}{\ensuremath{\stackrel{\cdot}{\sim}}}
\newcommand{\asim}{\ensuremath{\stackrel{\,\mathrm{a}}{\sim}}}
\newcommand {\plim}{\ensuremath{\operatorname*{plim}}}
\newcommand{\Pto}{\ensuremath{\stackrel{\textup{P}}{\longrightarrow}}}
\newcommand{\kiw}[2]{#1\ensuremath{\stackrel{\text{P}}{\longrightarrow}}#2}
\newcommand{\Dto}{\ensuremath{\stackrel{\text{D}}{\longrightarrow}}}
\newcommand{\iVto}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\iqmto}{\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}}
\newcommand{\kiqm}[2]{#1\ensuremath{\stackrel{\text{i.q.M.}}{\longrightarrow}}#2}
\newcommand{\kiv}{\ensuremath{\stackrel{\text{i.V.}}{\longrightarrow}}}
\newcommand{\Var}{\operatorname{Var}}
\newcommand{\var}{\operatorname{Var}}
\newcommand{\fVar}{\ensuremath{\mathbf{Var}}}
\newcommand{\fvar}{\ensuremath{\mathbf{Var}}}
\newcommand{\Corr}{\operatorname{Corr}}
\newcommand{\corr}{\operatorname{Corr}}
\newcommand{\cor}{\operatorname{Cor}}
\newcommand{\fCorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fcorr}{\ensuremath{\mathbf{Corr}}}
\newcommand{\fE}{\ensuremath{\mathbf{E}}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\Cov}{\operatorname{Cov}}
\newcommand{\cov}{\operatorname{Cov}}
\newcommand{\fCov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\fcov}{\ensuremath{\mathbf{Cov}}}
\newcommand{\MSE}{\operatorname{MSE}}
%------------- Fette grosse Buchstaben im Mathemodus -----------
\newcommand{\mbA}{\mathbf{A}}
\newcommand{\mbB}{\mathbf{B}}
\newcommand{\mbC}{\mathbf{C}}
\newcommand{\mbD}{\mathbf{D}}
\newcommand{\mbE}{\mathbf{E}}
\newcommand{\mbF}{\mathbf{F}}
\newcommand{\mbG}{\mathbf{G}}
\newcommand{\mbH}{\mathbf{H}}
\newcommand{\mbI}{\mathbf{I}}
\newcommand{\mbJ}{\mathbf{J}}
\newcommand{\mbK}{\mathbf{K}}
\newcommand{\mbL}{\mathbf{L}}
\newcommand{\mbM}{\mathbf{M}}
\newcommand{\mbN}{\mathbf{N}}
\newcommand{\mbO}{\mathbf{O}}
\newcommand{\mbP}{\mathbf{P}}
\newcommand{\mbQ}{\mathbf{Q}}
\newcommand{\mbR}{\mathbf{R}}
\newcommand{\mbS}{\mathbf{S}}
\newcommand{\mbT}{\mathbf{T}}
\newcommand{\mbU}{\mathbf{U}}
\newcommand{\mbV}{\mathbf{V}}
\newcommand{\mbW}{\mathbf{W}}
\newcommand{\mbX}{\mathbf{X}}
\newcommand{\mbY}{\mathbf{Y}}
\newcommand{\mbZ}{\mathbf{Z}}
%------------- Fette kleine Buchstaben im Mathemodus -----------
\newcommand{\mba}{\mathbf{a}}
\newcommand{\mbb}{\mathbf{b}}
\newcommand{\mbc}{\mathbf{c}}
\newcommand{\mbd}{\mathbf{d}}
\newcommand{\mbe}{\mathbf{e}}
\newcommand{\mbf}{\mathbf{f}}
\newcommand{\mbg}{\mathbf{g}}
\newcommand{\mbh}{\mathbf{h}}
\newcommand{\mbi}{\mathbf{i}}
\newcommand{\mbj}{\mathbf{j}}
\newcommand{\mbk}{\mathbf{k}}
\newcommand{\mbl}{\mathbf{l}}
\newcommand{\mbm}{\mathbf{m}}
\newcommand{\mbn}{\mathbf{n}}
\newcommand{\mbo}{\mathbf{o}}
\newcommand{\mbp}{\mathbf{p}}
\newcommand{\mbq}{\mathbf{q}}
\newcommand{\mbr}{\mathbf{r}}
\newcommand{\mbs}{\mathbf{s}}
\newcommand{\mbt}{\mathbf{t}}
\newcommand{\mbu}{\mathbf{u}}
\newcommand{\mbv}{\mathbf{v}}
\newcommand{\mbw}{\mathbf{w}}
\newcommand{\mbx}{\mathbf{x}}
\newcommand{\mby}{\mathbf{y}}
\newcommand{\mbz}{\mathbf{z}}
%----- Fette Null und fette Eins --------------------------
\newcommand{\fatnull}{\mathbf{0}}
\newcommand{\fateins}{\mathbf{1}}
%----- Fettes Nabla --------------------------
\newcommand{\bnabla}{\boldsymbol{\nabla}}
%----- Fette grosse griechische Buchstaben im Mathemodus -----
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%----- Fette kleine griechische Buchstaben im Mathemodus -----
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\beps}{\boldsymbol{\varepsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\boldeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bvrho}{\boldsymbol{\varrho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bvphi}{\boldsymbol{\varphi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mcA}{\mathcal{A}}
\newcommand{\mcB}{\mathcal{B}}
\newcommand{\mcC}{\mathcal{C}}
\newcommand{\mcD}{\mathcal{D}}
\newcommand{\mcE}{\mathcal{E}}
\newcommand{\mcF}{\mathcal{F}}
\newcommand{\mcG}{\mathcal{G}}
\newcommand{\mcH}{\mathcal{H}}
\newcommand{\mcI}{\mathcal{I}}
\newcommand{\mcJ}{\mathcal{J}}
\newcommand{\mcK}{\mathcal{K}}
\newcommand{\mcL}{\mathcal{L}}
\newcommand{\mcM}{\mathcal{M}}
\newcommand{\mcN}{\mathcal{N}}
\newcommand{\mcO}{\mathcal{O}}
\newcommand{\mcP}{\mathcal{P}}
\newcommand{\mcQ}{\mathcal{Q}}
\newcommand{\mcR}{\mathcal{R}}
\newcommand{\mcS}{\mathcal{S}}
\newcommand{\mcT}{\mathcal{T}}
\newcommand{\mcU}{\mathcal{U}}
\newcommand{\mcV}{\mathcal{V}}
\newcommand{\mcW}{\mathcal{W}}
\newcommand{\mcX}{\mathcal{X}}
\newcommand{\mcY}{\mathcal{Y}}
\newcommand{\mcZ}{\mathcal{Z}}
%----------- Kalligraphische Buchstaben im Mathemodus
\newcommand{\mca}{\mathcal{A}}
\newcommand{\mcb}{\mathcal{B}}
\newcommand{\mcc}{\mathcal{C}}
\newcommand{\mcd}{\mathcal{D}}
\newcommand{\mce}{\mathcal{E}}
\newcommand{\mcf}{\mathcal{F}}
\newcommand{\mcg}{\mathcal{G}}
\newcommand{\mch}{\mathcal{H}}
\newcommand{\mci}{\mathcal{I}}
\newcommand{\mcj}{\mathcal{J}}
\newcommand{\mck}{\mathcal{K}}
\newcommand{\mcl}{\mathcal{L}}
\newcommand{\mcm}{\mathcal{M}}
\newcommand{\mcn}{\mathcal{N}}
\newcommand{\mco}{\mathcal{O}}
\newcommand{\mcp}{\mathcal{P}}
\newcommand{\mcq}{\mathcal{Q}}
\newcommand{\mcr}{\mathcal{R}}
\newcommand{\mcs}{\mathcal{S}}
\newcommand{\mct}{\mathcal{T}}
\newcommand{\mcu}{\mathcal{U}}
\newcommand{\mcv}{\mathcal{V}}
\newcommand{\mcw}{\mathcal{W}}
\newcommand{\mcx}{\mathcal{X}}
\newcommand{\mcy}{\mathcal{Y}}
\newcommand{\mcz}{\mathcal{Z}}
%---------- Doppelsumme ------------------------------------------
\newcommand{\dblsum}[1]{\ensuremath{\mathop{\sum\sum}\limits_{#1}}}
%---------- \argmin und \argmax ------------------------------
\newcommand{\argmin}{\ensuremath{\operatorname*{arg{}min}}}
\newcommand{\argmax}{\ensuremath{\operatorname*{arg{}max}}}
%---------- Folgen ------------------------------------------
\newcommand{\avec}[2]{#1_1,\ldots,#1_{#2}}
\newcommand{\avecc}[2]{\ensuremath{#1_1,#1_2,\ldots,#1_{#2}}}
\newcommand{\aveccc}[3]{\ensuremath{(#1_{#2},\ldots,#1_{#3})}}
%---------- Geordnete Werte ---------------------------------------
\newcommand{\ord}[2]{\ensuremath{#1_{(1)},\ldots,#1_{(#2)}}}
\newcommand{\ordd}[2]{\ensuremath{#1_{(1)}\le#1_{(2)}\le\cdots\le#1_{(#2)}}}
\newcommand{\ordstat}[2]{\ensuremath{#1_{(#2)}}}
\newcommand{\ordne}[3]{\ensuremath{#1_{(1)}#3 #1_{(2)}#3\dots#3#1_{(#2)}}}
\)
\quoteon(2023-06-09 17:10 - Carly2004 in Beitrag No. 9)
Aus der Markov-Ungleichung mit
f(x)=e^tx mit t>0
\quoteoff
Das ergibt fuer mich keinen Sinn.
Hier finde ich fuer eine Zufallsvariable $X$:
\[P(|X|\ge a)\le\frac{\E[|X|]}{a}\]
mit $a>0$. Angewendet auf $S_n=|S_n|$ ergibt sich
\[P\left(S_n\ge\dfrac{n(1+\delta)}{\lambda}\right)\le\frac{\E[S_n]\lambda}{n(1+\delta)}\,.\]
\(\endgroup\)
|
Profil
|
| Carly2004 hat die Antworten auf ihre/seine Frage gesehen. |
|
All logos and trademarks in this site are property of their respective owner. The comments are property of their posters, all the rest © 2001-2023 by Matroids Matheplanet
This web site was originally made with PHP-Nuke, a former web portal system written in PHP that seems no longer to be maintained nor supported. PHP-Nuke is Free Software released under the GNU/GPL license.
Ich distanziere mich von rechtswidrigen oder anstößigen Inhalten, die sich trotz aufmerksamer Prüfung hinter hier verwendeten Links verbergen mögen.
Lesen Sie die
Nutzungsbedingungen,
die Distanzierung,
die Datenschutzerklärung und das Impressum.
[Seitenanfang]
|
Home / Seite ohne Frame
Wie unterstütze ich den Matheplaneten mit Geld?
