Chapter 10, Problem 10.7P

Let F be the distribution function $F\left(x\right)=x^{n}0<x<1$

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

b. Let $U_1,\mathrm{...},U_n$ be independent random numbers. Show that $P\left\{\max \left(U_1,\mathrm{...},U_n\right)\le x\right\}=x^n$

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