Problem 5
Suppose X and Y have joint probability distribution fXY (x, y) = c(x 2 +xy) on [0, 2]×[0, 2], i.e. 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2.
(a) Find c.
(b) Find the joint cdf FXY (x, y).
(c) Find the marginal cumulative distribution functions FX(x) and FY (y) and the marginal pdf fX(x) and fY (y).
(d) Find E(X) and Var(X).
(e) Find E(Y ) and Var(Y ).
(f) Find the covariance and correlation of X and Y .
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