The joint cumulative distribution function for ( X , Y ) ( X , Y ) is given by F ( x , y )

The joint cumulative distribution function for $(X,Y)$ is given by

$F(x,y)=(1-e^{-x/10}-e^{-y/2}+e^{-(x+5y)/10})I_{(0,\infty )}\left(x\right)I_{(0,\infty )}\left(y\right)$.

a. Find the joint density function of $(X,Y)$.

b. Find the marginal density function of $X$.

c. Find the marginal cumulative distribution function of $X$.