MA340 Study Guide - Moment-Generating Function, Probability Mass Function, Xm Satellite Radio
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Ma340 quiz: july 25-26, 2013 solutions: let x have probability mass function f(x) = (. 3)(. 7)x 1, x = 1, 2, 3, . Be sure to state (and justify) its domain. Hint: at some point you"re going to want to factor out (. 3)et from each term in a series. The series above is a geometric series and will converge if and only if |. 7et| < 1, which is equivalent to. Provided t lies in the appropriate range the sum of the series is. 1 . 7et , t < ln(10/7) : suppose that x has moment generating function. 1 (. 1)et , t < ln(10) . (a) use mx (or a suitable transformation of mx) to nd the mean and variance of x. 9et (1 . 1et)2 , (. 9et)(1 + . 1et) (1 . 1et)3. X(0) (. 9)(1 + . 1) (1 . 1)3 (. 9)(1. 1) (. 9)3. So the mean of x is 10/9 and the variance is.
