1. ## Statistics

Let $\displaystyle N,X_1,X_2,...$ be independent random variables where N has a Poisson distribution with mean 3 while $\displaystyle X_1,X_2,...$ each has a Poisson distribution with mean 7.

Determine $\displaystyle E[\sum^{N}_{i=1} X_i]$ and also the variance of $\displaystyle \sum^{N}_{i=1} X_i$

Any help or hints would be most appreciated. Thanks.

2. Originally Posted by Len
Let $\displaystyle N,X_1,X_2,...$ be independent random variables where N has a Poisson distribution with mean 3 while $\displaystyle X_1,X_2,...$ each has a Poisson distribution with mean 7.

Determine $\displaystyle E[\sum^{N}_{i=1} X_i]$ and also the variance of $\displaystyle \sum^{N}_{i=1} X_i$

Any help or hints would be most appreciated. Thanks.