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Unformatted text preview: X and | X | . In what range is each moment generating function deﬁned? ( b ) Use the moment generating function computed in part ( a ) to calculate the mean and the variance of X . Problem 4 Suppose that X is a nonnegative random variable with EX = 10, Var( X ) = 4. ( a ) Based only on the above information, what is the sharpest upper bound you can obtain on P ( X > 11)? 1 ( b ) Let X 1 ,X 2 ,...,X n be independent and identically disributed random variables each with the same distribution as X , and Y n = ( X 1 + ... + X n ) /n the corresponding sample mean. Based on the above information, how large should the sample size n be to guarantee that P ( Y n > 11) ≤ . 05? 2...
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- Probability theory, continuous random variable, continuous random vector, nonnegative random variable