Question: Consider a pair of random variables X, Y with constant joint density on the quadrilateral with vertices (0, 0), (2, 0), (2, 6), (0, 12).

Consider a pair of random variables X, Y with constant joint density on the quadrilateral with vertices (0, 0), (2, 0), (2, 6), (0, 12).
a. For 0 ≤ y ≤ 6, find the conditional density fX|Y (x | y) of X, given Y = y.
b. For 6 ≤ y ≤ 12, find the conditional density fX|Y(x | y) of X, given Y = y.
c. Find the conditional probability that X ≤ 1, given 3 ≤ Y ≤ 9.

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