Let U be a uniform (0,1) random variable, and let a < b be constants.
(a) Show that if b > 0, then bU is uniformly distributed on (0, b), and if b < 0, then bU is uniformly distributed on (0,b).
(b) Show that a + U is uniformly distributed on (a, 1 + a).
(c) What function of U is uniformly distributed on (a, b)?
(d) Show that min(U, 1 − U) is a uniform (0,1/2) random variable.
(e) Show that max(U, 1 − U) is a uniform (1 /2,1) random variable.
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