(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X_{1}...X_{N}be independent and identically distributed random variables, N is a non-negative integer valued random variable. Let Z = X_{1}+ ... + X_{N}(assume when N=0 Z=0).

1. Find E(Z)

2. Show var(Z) = var(N)E(X_{1})^{2}+ E(N)var(X_{1})

2. Relevant equations

E(Z) = E_{X}(E(X|Z))

Law of total variance: var(Z) = E_{X}(var(Z|X)) + Var_{X}(E(Z|X))

3. The attempt at a solution

1. I think I have managed this, I got E(N)E(X)

2. I'm unsure how to tackle this one, I know var(Z) = E(Z^{2}) - E(Z)^{2}, and I know E(Z)^{2}but I don't know how to calculate the other, or if I should be using the equation above, and if so, how.

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# Homework Help: Expectation and variance of a random number of random variables

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