A population consists of three housing units, where the number of rooms in each unit is 1, 3 and 4, respectively.

a) What is the population distribution of the number of rooms?

b) What are the mean and standard deviation of the population distribution?

c) A random sample without replacement of 2 housing units is picked from the population. Give the sampling distribution of the sample mean.

d) Find the mean of the sampling distribution of the sample mean and compare it with the mean of the population distribution in b).

e) A random sample with replacement of 2 housing units is picked from the population. Give the sampling distribution of the sample standard deviation