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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Autumn Brock

Mathematics

16 February, 13:39

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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Glenn Knapp · Answer 1

11186 In this exercise, you will write some code that reads n unique (no duplicates!) non-negative integers, each one less than fifty (50). Your code will print them in sorted order without using any nested loops- - potentially very efficient!

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