In each of the following cases, give an algorithm that uses exactly one random number for generating a random variate with the same distribution as X.
(a) X = min{U1, U2}, where U1 and U2 are IID U(0, 1).
(b) X = max{U1, U2}, where U1 and U2 are IID U(0, 1).
(c) X = min{Y1, Y2}, where Y1 and Y2 are IID exponential with common mean β.
Compare (a) and (b) with Prob. 8.7. Compare your one-U algorithms in (a) through (c) with the direct ones of actually generating the Ui’s or Yi’s and then taking the minimum or maximum.
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