1. ## conditional

given that f(x,y) = exp (-(x+y)) for x>0 and y>0,

for any y>0, what is the conditional density function of X given that Y=y?

my working:

from how i see it, its the
marginal density of X divided by the the marginal density of X = 1

what is wrong with my reasoning? help is greatly appreciated.

thank you!

2. BY inspection the two rvs are indep.

so $f(x|y)=f(x)=e^{-x}$ where x>0