9. Suppose we have a method to simulate random variables from the distributions F and F2. Explain...

9. Suppose we have a method to simulate random variables from the distributions F₁ and F2. Explain how to simulate from the distribution

$$

F(x) = pF₁(x) + (1-p)F(x)

\qquad 0 < p < 1

$$

Give a method for simulating from

$$

\begin{aligned}

F(x) &= \begin{cases}

\left(\frac{1}{3}\right) (1 - e^{-3x}) + \frac{x}{3} & 0 < x \le 1 \\

\left(\frac{1}{3}\right) (1 - e^{-3x}) + \frac{1}{3} & x > 1

\end{cases}

\end{aligned}

$$