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Unformatted text preview: STAT/MATH 511 SUMMER, 2010 EXAM 2 GROUND RULES: This exam contains 7 questions; each question is worth its enumerated value. The maximum number of points on this exam is 100. You may use a calculator if you wish, but SHOW ALL OF YOUR WORK AND EXPLAIN ALL OF YOUR REASONING!!! Any discussion or otherwise inappropriate communication between ex- aminees will be dealt with severely. HONOR PLEDGE FOR THIS EXAM: After you have finished the exam, please read the following statement and sign your name below it. I promise that I did not discuss any aspect of this exam with any- one other than the instructor, that I neither gave nor received any unauthorized assistance on this exam, and that the work presented herein is entirely my own. i 1.(30 Possible Points) The number of claims per week at an insurance com- pany is a random variable Y . Suppose that Y has probability mass function p Y ( y ) = ( ce- 2 y , y = 0 , 1 , 2 ,... , otherwise. (a). Find c such that p Y ( y ) is a valid probability mass function. (b). What is the probability that there are at least 2 claims in a given week? (c). Show that the moment generating function (mgf) of Y is given by m Y ( t ) = c (1- e t- 2 )- 1 , for values of t < 2. Make sure you argue why t < 2....
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This note was uploaded on 06/17/2010 for the course MATH math 231 taught by Professor Hart during the Spring '10 term at Academy of Art University.
- Spring '10