Question: 5. The joint probability density function (pdf) of two random variable X and Y is given by () (1 + zy), 05x1, 0Lyk1 fx.y (x,

5. The joint probability density function (pdf) of two random variable X and Y is given by () (1 + zy), 05x1, 0Lyk1 fx.y (x, y) = otherwise. (a) Find the marginal probability density functions for X and Y. (b) Are X and Y independent random variables? Justify your answer. (c) Show that the expectation of XY is 13/45, that is E(XY) - 13/45. (d) Given that E(X) - E(Y ) - 5/15 and Var(X) = Var(Y) = 43/450, calculate the covariance and correlation of X and Y. Comment on the direction and strength of the linear association between X and Y

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