DES Chapter 8

  • Question 5:

$ F(x)={ 0,x-3\ 1/2+x/6,-34 $

\(\quad\ X\quad =\left\{ 6R-3,\quad 0<R\le 1/2\\ \\ 4\sqrt { 2R-1 } ,\quad 1/2\quad <R\quad \le 1 \right\)

r = runif(100000, 0, 1)
x = ifelse(r <= 0.5, 6*r-3, 4*sqrt(2*r-1))
## Warning in sqrt(2 * r - 1): NaNs produced
par(mfrow = c(1,2))
hist(x, col=blues9)