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# . Complete both parts (a) and (b) below. ). In1 (a) Let X11, X12, ..., X be a random sample of size n from

## . Complete both parts (a) and (b) below. ). In1 (a) Let X11, X12, ..., X be a random sample of size n from a population with mean and variance . Let X21, X22,..., X2n2 be a random sample of size n from another population with mean and variance . The two samples are independent. Consider the sample means X = X1 and X2 X2. Show that n1 = n2 E(X1 X2) = 2 and Var(X1 X2) = 01 02 + n1 n2 Hint: Use the known results for the mean and variance of a sample mean. (b) If the first random sample X11, X12,..., Xin are from Normal (, 02) population, and the second random sample X21, X22, ..., X2n2 are from Normal (2, 2) population. Use the MGF technique to show that XX2~Normal ( - 2, + n1 n2 Hint: Use the known distribution for a sample mean, when the samples come from a normal population.

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