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Please show calculations of how you got the answers Exercise 6.34..pdf

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This document asks to (a) find the joint and marginal density functions of random variables X and Y which are uniformly distributed on a quadrilateral region D, (b) calculate the expected values of X and Y, and (c) determine if X and Y are independent.

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Please show calculations of how you got the answers Exercise 6.34. Let (X,Y) be a uniformly distributed random point on the quadrilateral D with vertices (0,0),(2,0),(1,1) and (0,1). (a) Find the joint density function of (X,Y) and the marginal density functions of X and Y. (b) Find E[X] and E[Y]. (c) Are X and Y independent?

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