Let X1 and X2 be independent and identical normal random variables with common mean 3 and standard deviation 1. Consider the sample mean U = Xi+X2 a. What is the moment-generating function my (t) of U? [Hint: Refer to Proposition 3.1, mu (t) = mx,(G)mx, (t) - ] b. What is the distribution of U? c. Find the probability that the observed sample mean is between 2.8 and 3.2.

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