Question

Generate a population of size N= 10000 from an exponential distribution with mean θ= 10.

a. Generate 1000 samples of sizen= 200 from the population and plot the density of the sample means.

b. Generate a single sample of sizen= 200. Resample with sizen= 200 with replacement fromthis single sample 1000 times. Plot the density of the resample means.

c. Comment on the two densities you have plotted

Answer 1

I will use R to answer this question.

Following is the R code.

#########################

set.seed(122337)
pop=rexp(10000,rate=1/10)
######a
means=array(dim=1)
for(i in 1:1000)
{
samp=sample(size=200,x=pop,replace=TRUE)
means[i]=mean(samp)
}
######b
samp1=sample(size=200,x=pop,replace=TRUE)
means_re=array(dim=1)
for(i in 1:1000)
{
samp=sample(x=samp1,size=200,replace=TRUE)
means_re[i]=mean(samp)
}
par(mfrow=c(2,1))
hist(means,freq=FALSE)
hist(means_re,freq=FALSE)

###########

Running the whole code, we can se that both are giving good estimates of the Exponential densities sample means. However, the resampled mean is a bit deviated from the value of 10