Chapter 10, Problem 10.9P

Suppose we have a method for simulating random variables from the distributions F₁ and F₂. Explain how to simulate from the distribution $F\left(x\right)=p{F}_1\left(x\right)+\left(1-p\right)F_2\left(x\right)0<p<1$

Give a method for simulating from $F\left(x\right)=\{\begin{array}{c}\frac{1}{3}\left(1-e^{-3x}\right)+\frac{2}{3}x0<x\le 1\\ 4\frac{1}{3}\left(1-e^{-3x}\right)+\frac{2}{3}x>1\end{array}$