diff --git a/ch04.r b/ch04.r index 98c4c9d..de58f57 100644 --- a/ch04.r +++ b/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))