Consider the hypothetical population below (this population is also used in Example
2.2). Consider the stratification below, with N1 = N2 = 4. The population is:

Consider the stratified sampling design in which n1 = n2 = 2.
a. Write out all possible SRSs of size 2 from stratum 1, and find the probability of each sample. Do the same for stratum 2.
b. Using your work in (a), find the sampling distribution of ṫstr.
c. Find the mean and variance of the sampling distribution of ṫstr. How do these compare to the mean and variance in Example 2.2?