################## Example 1 ######################

# R code to approximate sampling distribution of X-bar
# when taking sample of size 4 from an exponential(1) distn:

my.m <- 1000
my.n <- 4
sample.matrix<-matrix(rexp(my.m*my.n, 1), nrow=my.m, ncol=my.n)
# Each row will be a sample of size 4
# There will be 1000 of these simulated "samples"

my.xbar.values <- apply(sample.matrix, 1, mean)

par(mfrow=c(2,2))
hist(my.xbar.values)
plot(density(my.xbar.values))

# 95% of sample mean values are between these two numbers:

lower.upper <- quantile(my.xbar.values, probs=c(0.025, 0.975))

print(lower.upper)

################## Example 2 ######################

# R code to approximate sampling distribution of sample midrange
# when taking sample of size 4 from an exponential(1) distn:

find.midrange<-function(x){
range.vector <- range(x)
## Note midrange formula:
#The following is correct:
my.midrange <- sum(range.vector)/2
return(my.midrange)
}


my.midrange.values <- apply(sample.matrix, 1, find.midrange)

hist(my.midrange.values)
plot(density(my.midrange.values))

# 95% of midrange values are between these two numbers:

lower.upper <- quantile(my.midrange.values, probs=c(0.025, 0.975))

print(lower.upper)


par(mfrow=c(1,1))