Chapter 8, Problem 5

Given the following cdf for a continuous variable with range from -3 to 4, develop a generator for the variable.

\[F(x) = \begin{cases} 0, x \le -3 \\ \frac{1}{2} + \frac{x}{6}, -3 \le x \le 0 \\ \frac{1}{2} + \frac{x^2}{32}, 0 \lt x \le 4 \\ 1, x \gt 4 \end{cases}\]

set.seed <- 1023

r <- runif(1000, 0, 1)
x = ifelse(r <= 0.5, 6*r-3, 4*sqrt(2*r-1))

head(x)
## [1]  3.5650211 -0.6632568 -0.9188833  3.8978907 -1.2331805 -0.3048793
hist(x)