20. Suppose that X1, . . . , Xn is a sample from a distribution whose mean is , variance is 2, and whose moment-generating

20. Suppose that X1, . . . , Xn is a sample from a distribution whose mean is μ, variance is σ2, and whose moment-generating function exists. Show, using the method of moment-generating functions, that the mean and variance of the sample sum T are nμ

and nσ2, respectively. Also use the method of moment-generating functions to show that the mean and variance of the sample mean ¯X are μ and σ2/n, respectively.