Solutions Probability

Let N, X1, X2,… be independent random variables where N has a Poisson distribution with mean 5 while

Question: Let N, X1, X2,… be independent random variables where N has a Poisson distribution with mean 5 while X1, X2,…each has a Poisson distribution with mean 2.

(a) Determine E[N \[\sum\limits_{i=1}^{N}{{{X}_{i}}}\] ]

(b) Determine the variance of \[\sum\limits_{i=1}^{N}{{{X}_{i}}}\]

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