Question: S Walds identity. Let .Xi /i1 be i.i.d. real random variables in L1 and let be a ZCvalued random variable with E./ < 1.

S Wald’s identity. Let .Xi /i1 be i.i.d. real random variables in L1 and let be a ZCvalued random variable with E./ < 1. Suppose that, for every n 2 N, the event ¹ nº is independent of Xn. Show that the random variable S D P

iD1 Xi has an expectation, and E.S / D E./E.X1/ :

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