Statistik 3 - Beispiel 3

From StatWiki
Jump to: navigation, search

Zumindest (a)

 \operatorname{E}(X_i) = 0

 \operatorname{Cov}(X_i, X_j) = 0, i \ne j

 \operatorname{Cov}(X_i,X_j) = \operatorname{E}( (X_i - \operatorname{E}(X_i)) (X_j - \operatorname{E}(X_j) ) = \operatorname{E}(X_i X_j)


\begin{matrix}
\operatorname{E}( (\sum X_i)^2 ) = 
\operatorname{E}( \sum X_i^2 + & \sum_i \sum_j & X_i X_j ) =  
\sum \operatorname{E}( X_i^2 ) + & \sum_i \sum_j & \underbrace{ \operatorname{E}( X_i X_j ) } & = 
\sum \operatorname{E}( X_i^2 ) \\
& i \ne j & & i \ne j & 0 &
\end{matrix}