# X ~ exp(theta=2)
# Want to generate 500 observations from X 

# inverse.cdf.r
###############

# generate 500 observations y_i, i=1,...,500, from a Unif(0,1) random variable
y <- runif(500, 0 , 1)

# plug the y_i values into the inverse cdf to obtain x_i, i=1,...,500
x <- -2 * log(1-y)

# plot true density 
grd <- seq(0,12,length=1000)
pdf("inverse-cdf.pdf")
plot(grd, 0.5*exp(-0.5*grd), type="l", xlab="x", ylab="f(x)", main="X ~ exp(theta=2)")
# make a "rug" with the generated values
rug(x)
dev.off()

# compute mean and variance of generated values
# these should be close to E(X)=theta=2 and Var(X)=theta^2=4
cat("mean(x): ",mean(x),"\n")
cat("var(x): ",var(x),"\n")

# invoking the program (and the output)
#######################################

# > source("inverse-cdf.r")
# mean(x):  2.073205 
# var(x):  3.865034