Given pdf $f(x,y)=x+y$, both $x$ and $y$ are in range $[0,1]$, we need to generate vectors $<x,y>$ from the distribution and verify.
I have found the CDF of the function and also the marginal pdf $fx$ and $fy$ for each case I tried taking the inverse transform of marginal pdfs but am not getting proper results using histogram analysis. Is there any other way?
One way is to first find the conditional distribution of $y$ given $x$ (try to figure this out by yourself through the joint pdf) and then simulate as follows: first simulate $x$ from its marginal, then simulate $y$ from the conditional distribution given the value of $x$.