# Stratified random sampling and its distribution

I'm learning stratified random sampling and I'm having hard time to solve this problem. consider the following population of six units:

x1=1, x2=2, x3=2, x4=4 x5=4 x6=5


Suppose units 2 3 4 and 5 are in one stratum and units 1 and 6 are in a second stratum. Take a simple random sample of 2 units from the first stratum and a simple random sample of 1 unit from the second stratum. What is the exact distribution of the stratified estimator for the population average?

So, possible mean of sample from first stratum is 2, 3 or 4 and from second stratum is 1 or 5. overall sample mean is

2/3 * 2 + 1/3 * 1 = 5/3
2/2 * 2 + 1/3 * 1 = 7/3
2/3 * 4 + 1/3 * 1 = 3
2/3 * 2 + 1/3 * 5 = 3
2/3 * 3 + 1/3 * 5 = 11/3
2/3 * 4 + 1/3 * 5 = 13/3


and each probability is 1/12, 4/12, 1/12, 1/12, 4/12, 1/12. Now what should I do for finding exact distribution?

• "possible mean of sample from first stratum is 2, 3 or 4 and from second stratum is 1 or 5" -- unless I misunderstood something, both those statements aren't correct. – Glen_b Jul 9 '14 at 8:58