# Question

Let F be the distribution function

F(x) = xn 0 < x < 1

(a) Give a method for simulating a random variable having distribution F that uses only a single random number.

(b) Let U1, . . . ,Un be independent random numbers. Show that

P{max(U1, . . . ,Un) ≤ x} = xn

(c) Use part (b) to give a second method of simulating a random variable having distribution F.

F(x) = xn 0 < x < 1

(a) Give a method for simulating a random variable having distribution F that uses only a single random number.

(b) Let U1, . . . ,Un be independent random numbers. Show that

P{max(U1, . . . ,Un) ≤ x} = xn

(c) Use part (b) to give a second method of simulating a random variable having distribution F.

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