# Statistics

• Mar 27th 2009, 10:42 AM
Len
Statistics
Let $N,X_1,X_2,...$ be independent random variables where N has a Poisson distribution with mean 3 while $X_1,X_2,...$ each has a Poisson distribution with mean 7.

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

Any help or hints would be most appreciated. Thanks.
• Mar 27th 2009, 07:07 PM
mr fantastic
Quote:

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

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

Any help or hints would be most appreciated. Thanks.