175HWSet1-2011 - page 57 of Introduction to Probability...

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Homework Set 1 Write legibly. Show your steps. Explain your reasoning. Simplify your answers. Due: Beginning of class on Monday, January 24, 2011 1) Define n M x = 1 0 x n x n q p . Calculate the matrix product n M x k M x+n . Your answer should be of the form ? M ? 2) Determine the moment generating function M S (t), where S is the random variable defined in #12.13 on page 394 of Actuarial Mathematics , 2 nd edition. 3) Actuarial Mathematics , 2 nd edition, page 393 #12.9. You are to use the convolution formula (2.3.7) on page 35 of Actuarial Mathematics or (2.18) on
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Unformatted text preview: page 57 of Introduction to Probability Models , 10 th edition. You will not receive any credit if you solve the problem by using (12.3.19). 4) Actuarial Mathematics , 2 nd edition, page 396 #12.23.a Here, X is a random variable whose moment-generating function exists. You may want to first do #79 on page 95 of Introduction to Probability Models , 10 th edition. 5) Introduction to Probability Models , 10 th edition, page 174 #14: Let X be uniform over (0, 1). Find the conditional expectation E[X | X < ]....
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