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Let X and Y have joint density f given by f(x, y) = cxy 0 ≤...

Let X and Y have joint density f given by f(x, y) = cxy 0 ≤ y ≤ x, 0 ≤ x ≤ 1.

(a) Determine the normalization constant c.

(b) Determine P(X + 2Y ≤ 1).

(c) Find E(X|Y = y).

(d) Find E(X).

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