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Mathematics, 16.03.2020 20:47 HalpMahOnMahH0meW0rk
The idea in Exercise 3.51 generalizes to give a new formula for the expected value of any nonnegative integer-valued random variable. Show that if the random variable X takes only nonnegative integers as its values then E(X) = X[infinity] k=1 P(X ≥ k). This holds even when E(X) = [infinity], in which case the sum on the right-hand side is infinite. Hint. Write P(X ≥ k) as P[infinity] i=k P(X = i) in the sum, and then switch the order of the two summations.
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The idea in Exercise 3.51 generalizes to give a new formula for the expected value of any nonnegativ...
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