7. In the following, F is the distribution function

$$

F(x) = x^r

\qquad 0 < x < \infty

$$

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

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

$$

P(max(U₁,..., U) ≤ x) = x^r

$$

(c) Use part

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