Chapter 9.1, Problem 6E

Prove that $u_1=x\begin{array}{c}2\\ 1\end{array}+x\begin{array}{c}2\\ 2\end{array}$ in the Box-Muller Rejection Method is a uniform random number on [0, 1]. (Hint: Show that for $0\le y\le 1$, the probability that $u_1\le y$ is equal to y. To do so, express it as the ratio of the disk area of radius $\sqrt{y}$ to the area of the unit circle.)