Add section 4.8

ch04.r

@@ -120,3 +120,29 @@ X3 = runif(N, 1, 6)
 Z = X1 + X2 + X3
 hist(Z, breaks=seq(2.5,18.5))
 
+# Chapter 4.8
+
+## Generating Gaussians from uniform
+
+# R code to generate Gaussian from uniform
+library(HDInterval)
+mu = 3
+sigma = 2
+U = runif(10000, 0, 1)
+gU = sigma * inverseCDF(U, pnorm) + mu;
+hist(U)
+hist(gU)
+
+# R code to generate exponential random variables
+lambda = 1
+U = runif(10000, 0, 1)
+gU = -(1/lambda)*log(1-U)
+
+# R code to generate the desired random variables
+U = runif(10000, 0, 1)
+gU = rep(0, 10000)
+gU[U >= 0.0 & U <= 0.1] = 1
+gU[U > 0.1 & U <= 0.6] = 2
+gU[U > 0.6 & U <= 0.9] = 3
+gU[U > 0.9 & U <= 1] = 4
+hist(gU)