# Question: Given the joint density Show that a Y x x 2 and X y

Given the joint density

Show that

(a) µY|x = x/2 and µX|y = 1+y / 2;

(b) E(XmYn) = 2 / (n + 1)(m + n + 2).

Also,

(c) verify the results of part (a) by substituting the values of µ1, µ2, σ1, σ2, and ρ, obtained with the formula of part (b), into the formulas of Theorem 14.1.

Show that

(a) µY|x = x/2 and µX|y = 1+y / 2;

(b) E(XmYn) = 2 / (n + 1)(m + n + 2).

Also,

(c) verify the results of part (a) by substituting the values of µ1, µ2, σ1, σ2, and ρ, obtained with the formula of part (b), into the formulas of Theorem 14.1.

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