Take a Random Sample of Size N = 2, Without $\bar{x}$

Essay

Take a random sample of size n = 2, without replacement, from
{0, 2, 4, 6}. Let $\bar{x}$ = mean of the two numbers selected.
(a) List the six possible $\bar{s}$ amples and the associated value of the sample mean.
(b) Construct the sampling distribution of $\bar{x}$ .
(c) Obtain the expected value of $\bar{x}$ using the sampling distribu- tion in Part b.
(d) Obtain the variance of $\bar{x}$ using the sampling distribution in Part b.