Exam P Practice Problem 46 – Finding Moment of a Sum

Problem 46-A

Suppose that X and Y are random losses that are jointly distributed with the following density function:

      \displaystyle f(x,y)=\frac{1}{40} \ (4-x) \ \ \ \ \ \ 0<x<4, \ \ 0<y<5

Find the second moment of the sum of the two losses.

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Problem 46-B

Suppose that X and Y are random losses that are jointly distributed with the following density function:

      \displaystyle f(x,y)=32 \ x^2 \ y \ e^{-2 \ (x \ + \ y)} \ \ \ \ \ \ 0<x<\infty, \ \ 0<y<\infty

Find the second moment of the sum of the two losses.

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Answers

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\copyright \ 2013

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