# HW4 - AMS 410 Actuarial Mathematics Fall 2009 Homework 4...

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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Homework 4: Joint Distribution Due: 11/12/2009 1. Discrete, marginal. Let X and Y be discrete random variables with joint probability function p ( x,y ) = ( 2 x + y 12 for ( x,y ) = (0 , 1) , (0 , 2) , (1 , 2) , (1 , 3) , otherwise . Determine the marginal probability function of X. 2. Discrete, variance. A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold, and suppose that P ( X = x,Y = y ) = 1 6 for ( x,y ) = (0 , 0) , 1 12 for ( x,y ) = (1 , 0) , 1 6 for ( x,y ) = (1 , 1) , 1 12 for ( x,y ) = (2 , 0) , 1 3 for ( x,y ) = (2 , 1) , 1 6 for ( x,y ) = (2 , 2) . What is the variance of X ?...
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HW4 - AMS 410 Actuarial Mathematics Fall 2009 Homework 4...

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