Question: Let X1, X2, . . . , X40 be independent identically distributed random variables such that the possible values of the Xj are 1, 2,

Let X1, X2, . . . , X40 be independent identically distributed random variables such that the possible values of the Xj are 1, 2, and 3. Suppose that P(Xj = 1) = P(Xj = 2) = 1 6 . (a) Compute the expected value and variance of Xj . (b) Let S = X1 + X2 + X40. Using the Central Limit Theorem, approximate P(98 X 106).

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