Add chapter 4.6

ch04.r

@@ -82,4 +82,41 @@ lines(x, F1, lwd=4, col="blue")
 lines(x, F2, lwd=4, col="red")
 legend(0, 1, legend=c(expression(paste(lambda, "=5")), expression(paste(lambda, "=2"))), col=c("red", "blue"), lty=1:1)
 
+# Chapter 4.6
+
+## PDF and CDF of a Gaussian random variable
+
+# R code to generate a Gaussian PDF
+x = seq(-10, 10, (10+10)/1000)
+mu = 0; sigma = 1;
+f = dnorm(x, mu, sigma)
+plot(x, f, type="n")
+lines(x, f, lwd=4, col="blue")
+
+# R code to generate standard Gaussian PDF and CDF
+x = seq(-5, 5, (5+5)/1000)
+f = dnorm(x)
+F = pnorm(x)
+plot(x, f)
+plot(x, F)
+
+# R code to verify standardised Gaussian
+x = seq(-5, 5, (5+5)/1000)
+mu = 3; sigma = 2;
+f1 = dnorm((x-mu)/sigma, 0, 1) # Standardised
+f2 = dnorm(x, mu, sigma) # Raw
+
+# R code to compute skewness and kurtosis
+library(e1071)
+X = rgamma(10000, 3, 5)
+s = skewness(X)
+k = kurtosis(X)
+
+# R code to show the histogram of Z = X1 + X2 + X3
+N = 10000
+X1 = runif(N, 1, 6)
+X2 = runif(N, 1, 6)
+X3 = runif(N, 1, 6)
+Z = X1 + X2 + X3
+hist(Z, breaks=seq(2.5,17.5))