1. Law of Total Expectation The so-called Wald's Identity states the following: Let X1, X2,….. be a sequence of independent and identically distributed random variables with finite mean. Let further N be a nonnegative integer-valued random variable independent of the X1, X2,... with finite mean. We define the random sum SN = X1 ++ XN. Then E[SN] = E[N] E[X1]. Prove Wald's identity by conditioning on {N = n} and by using the law of total expectation.

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