Let X and Y be two continuous random variables with joint pdf 2 f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3, and f(x, y) = 0 otherwise. (a) Find the value of c. (b) Find the probability P(1 ≤ X ≤ 2, 0 ≤ Y ≤ 1). (c) Determine the joint cdf of X and Y for a and b between 0 and 3. (d) Find marginal cdf FX(a) for a between 0 and 1. (e) Find the marginal pdf fX(x) directly from f(x, y) and check that it is the derivative of FX(x).

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Let X and Y be two continuous random variables with joint pdf
2 f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
and f(x, y) = 0 otherwise.
(a) Find the value of c.
(b) Find the probability P(1 ≤ X ≤ 2, 0 ≤ Y ≤ 1).
(c) Determine the joint cdf of X and Y for a and b between 0 and 3.
(d) Find marginal cdf FX(a) for a between 0 and 1.
(e) Find the marginal pdf fX(x) directly from f(x, y) and check that it is the derivative of
FX(x).

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