Μarginal Distributions of f(x,y)

#1
f(x,y) = e^(-x), 0<=x<inf, 0<=y<=1

To find the marginal PDFs here is what I did so far:
Marginal Distribution of x:
f(x) = integral from 0 to 1, e^(-x)dy = ye^(-x)
after evaluating I got e^(-x)

Marginal Distribution of y:
f(y) = integral from 0 to inf, e^(-x) = -e^(-x)
after evaluating I got 1

Am I evaluating each one using the wrong boundaries?
 

Dason

Ambassador to the humans
#2
No. Why do you think you did it wrong? It looks good to me. You just need to make sure to note what the support of your marginal distributions are.