Let X, Y have joint density fX.Y(x,y) = 14e-2x-7y for x > 0 and y > 0;

Question:

Let X, Y have joint density fX.Y(x,y) = 14e-2x-7y for x > 0 and y > 0; and fX,Y(x, y) = 0 otherwise.
a. For y > 0, find the conditional density fX|Y(x | y) of X given Y = y.
b. Find the conditional probability that X ≥ 1, given Y = 3.
c. Find the conditional probability that Y ≤ 1/5, given X = 2.7.