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In: Statistics and Probability

A two dimensional variable (X, Y) is uniformly distributed over the square having the vertices (2,...

A two dimensional variable (X, Y) is uniformly distributed over the square having the vertices (2, 0), (0, 2), (-2, 0), and (0, -2).
(i) Find the joint probability density function.
(ii) Find associated marginal and conditional distributions.
(iii) Find E(X), E(Y), Var(X), Var(Y).
(iv) Find E(Y|X) and E(X|Y).
(v) Calculate coefficient of correlation between X and Y.

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