My Math Forum Expected Payment problem

 January 14th, 2009, 07:03 AM #1 Member   Joined: Sep 2007 Posts: 77 Thanks: 0 Expected Payment problem A comprehensive auto insurance policy covers the damages to the automobile it insures and other vehicles involved in the accident. Suppose that X is the payment made to other parties and Y is the amount paid to the insured automobile. It is given that X and Y have a continuous joint probability density function as follows: fXY(x,y) = (3/2)y^2 for 0<=x<=2 and 0<=y<=1 and 0 otherwise Compute the expected payment to the policy holder involved in a car accident. Would this be E(X+Y)? E(X+Y)=E(X)+E(Y)? I think I would take the integral (with the limits given) but I'm just getting really confused... It's not working out with the x's and y's. If someone can help me get started that would be great!
 January 26th, 2009, 07:40 PM #2 Newbie   Joined: Jan 2009 From: Baton Rouge, LA Posts: 10 Thanks: 0 Re: Expected Payment problem Actually, what we are looking for is E[Y]. Thus all you need to do is find the marginal distribution of Y (by integrating the density function over all possible values for x), and then calculate the following integral: $\mathbb{E}(\bf{Y})= \int_{-\infty}^{\infty}yf_{Y}(y)dy$

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