a Find the marginal density function of X b Find the margina

(a) Find the marginal density function of X.

(b) Find the marginal density function of Y .

(c) Find the conditional density function of X given Y = y. (?given? is an alternative way to say ?conditional on?)

(d) Find the conditional density function of X given Y = 3.

(e) Find the conditional density function of Y given X = x.

(f) Find the conditional density function of Y given X = 2.

Solution

A) f(x)=integral(xe^(-x(y+1))dy=-e^(-x(y+1))+C