5-22. Given the joint probability density function f (x, y) = -k(x + 2y), 0 < x...

Question:

5-22. Given the joint probability density function f (x, y) = -k(x + 2y), 0 < x ≤ 2 and 0 < y ≤ 1;

0 elsewhere, find:

(a) The value of k

(b) The marginal distribution of X

(c) The cumulative distribution function

(d) P 1 ≤ X ≤ 2, 1 4

≤ Y ≤ 1 2

(e) The conditional density function of Y given X

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