Math 330 Statistics I Problem Set 2 Fall 2009 This assignment will be graded, so you must do your own work. You may use your class notes and text, but no outside references. You may not receive assistance from anyone else. If you have questions about the problems, see me. In order to receive full credit you must show clearly all steps necessary to obtain your answers. Be complete and precise. On the other hand, including irrelevant work may also result in loss of credit. Incoherent and illegible work will not be considered. Your work on these problems is due at the beginning of class on Friday, October 30, 2009. 1. Let Y have density function f ( y ) = cye − 2 y ,0 ≤ y < ∞ 0, elsewhere a) Find the value of c that makes f(y) a density function. b) Find the corresponding distribution function F ( y ) and sketch graphs of both f(y) and F ( y ). c) Find the moment-generating function for Y. d) Find the mean and variance for Y.
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