Let X be a random variable (on R) which has a density p(x). Assume that p(x) > 0 for any x E R. Let F1(s) = P(X < s) and F2(s) = P(X > s). Show that F1(X)~ Unif([0, 1])) and F2(X) ~ Unif([0, 1]). (please avoid using confusing notations P(X < X))

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A:

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