Let X and Y have joint density (a) By examining the joint density function can you guess

Question:

Let X and Y have joint density

zYe-s°/2, for r > 0, y > 0. f(r, y) = - -e-*ye- ye

(a) By examining the joint density function can you guess the conditional density of X given Y = y? (Treat y as a constant.) Confirm your guess.
(b) Similarly, first conjecture about the conditional distribution of Y given X = x. Find the conditional density.
(c) Find P(X <1|Y = 1).

Distribution
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