Unformatted text preview: answer. (6) Let X be a continuous random variable with a density f X ( x ) = 1 2 ex + e2 x , for x > 0. (a) Compute the moment generating function of X . What is the range on which the moment generating function is deﬁned? (b) Use the moment generating function from part ( a ) to compute the mean, the second moment and the variance of X . (7) (a) Derive the moment generating function of a Bernoulli random variable that takes possible values { , 1 } with probabilities p, 1p = q . (b) Derive the moment generating function of the binomial distribution ( n trials, success probability p ) and use it to derive the mean and the variance of a binomial random variable. (Save work. Use 7a to derive the mgf.) 1...
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 SAMORODNITSKY
 Probability theory, moment generating function

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