ex4_1_3.R

####################
# Exercise 4.1.3
####################
rm(list = ls()) # Clear work space

# Number of samples
N <- 1000

# Mean
mu <- 17

# Standard deviation
s <- 2

# Number of bins in histogram
NBins <- 50

# Generate samples from the Normal distribution
X <- rnorm(N, mean = mu, sd = s)

# Plot a histogram
{
  par(mfrow=c(1,1))
  res <- hist(X, breaks = NBins, freq = FALSE)
  x <- res$mids
  x <- seq(from = min(x), to = max(x), length.out = 1000)
  lines(x, dnorm(x, mean = mu, sd = s))
}

# Compute empirical mean and standard deviation
(mu_ <- mean(X))
(s_ <- sd(X))