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Expectation and variance of a random number of random variables
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csopi
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2
Jan26-10, 07:10 PM
P: 77
2. follows immediately from the total variance formula.
var Z=E ( var (Z|N)) + var (E (Z|N))
E ( var (Z|N))=E(N var (X1))=var(X1) E(N) -- by fixing N, Z is a sum of fixed number of Xi-s
var (E (Z|N))=var (N E(X1))=[E(X1)]^2*var(N)