Suppose that Y is a continuous random variable with density f (y) that is positive only
Chapter 4, Problem 4.34(choose chapter or problem)
Suppose that Y is a continuous random variable with density f (y) that is positive only if y 0. If F(y) is the distribution function, show that E(Y ) = " 0 y f (y) dy = " 0 [1 F(y)] dy. [Hint: If y > 0, y = # y 0 dt, and E(Y ) = # 0 y f (y) dy = # 0 %# y 0 dt& f (y) dy. Exchange the order of integration to obtain the desired result.]4
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