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MA340 (5)

# S2103_MA340_Q4.pdf

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School
Wilfrid Laurier University
Department
Mathematics
Course
MA340
Professor
Semester
Spring

Description
MA340 Quiz: July 25-26, 2013. Name: Student number: Instructions: Due in my o▯ce by 4:00 PM on Friday, July 26. Slip it under the door if I am not in. Please don’t hand in the ▯rst draft of your answer - i.e. solve the problems and then write up clear, easy-to-follow solutions in the space provided. 1. Let X have probability mass function x▯1 f(x) = (:3)(:7) ; x = 1;2;3;::: : Derive the moment generating function of X. Be sure to state (atd justify) its domain. Hint: At some point you’re going to want to factor out (:3)e from each term in a series. 2. Suppose that X has moment generating function (:9)e M (t) = ; t < ln(10) : X 1 ▯ (:1)e (a) Use M X (or a suitable transformation oX M ) to ▯nd the mean and variance of X. (b) Use M X (or a suitable transformation oX M ) to ▯nd the mean and variance of Y = e . (c) Use MX (or a suitable transformation oX M ) to ▯nd the moment generating function of Z = 4X ▯ 1. 3. Suppose I play three rounds of a certain game, and that I have a 75% chance of winning any round (the outcome of any given round has
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