Question: 15. Let g be a nonnegative real-valued function on R that R satisfies the relation g(t) dt = 1. Show that if, for

15. Let g be a nonnegative real-valued function on R that R satisfies the relation

∞

−∞

g(t) dt = 1. Show that if, for a random variable X, the random variable Y =

R X

−∞

g(t) dt is uniform, then g is the probability density function of X.

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