# Finding a marginal CDF

I am stuck finding a marginal CDF of X given the random variables $$X$$ and $$Y$$ with the joint density:

$$f_{XY}(x,y)=2e^{-(x+y)}$$ for $$0

$$f_X(x)=\int_x^{\infty} 2e^{-x-y} dy=2e^{-x}e^{-x}=2e^{-2x}$$ for $$0. Also $$F_X(x)=\int_0^{x} 2e^{-2t} dt =-e^{-2t}|_0^{x}=1-e^{-2x}, 0.
• Can you explain the second part ? $F_X(x)=1-e^{-2x}$ – i9-9980XE May 23 at 7:29
• Yes, $f_X$ is the marginal density of $F$ and $F_X$ is the marginal distribution function of $X$. – Kavi Rama Murthy May 23 at 7:34