Question: Suppose that X and Y are continuous random variables with the joint prob- ability density function f(x, y) = k(x + y) 0 for 0x1,

Suppose that X and Y are continuous random variables with the joint prob- ability density function

f(x, y) = k(x + y) 0 for 0x1, 0 y 2

f(x, y) = k(x + y) 0 for 0x1, 0 y 2 otherwise (a) Find k, E(X), E(Y), V(X), V(Y), and cov(X, Y). Are X and Y inde- pendent? (b) Find the marginal densities of X and Y. (c) Find the conditional density of X given Y and hence EXX | Y= and V(YX = D.

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