Let U~ U(0,1). Let a and b be constants with a < b, and let X = (b ? a)U+ a.
a. Find the cumulative distribution function of U.
b. Show that P(X ? x) = P(U ? (x?a)/(b ? a)).
c. Use the result of part (b) to show that X ~ U(a, b).
(a) The cumulative distribution function of U is
(b)
(c) The cdf of X is that of a random variable distributed U(a, b).
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