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I am given the following joint distribution of two random variables X and Y:

$$ f(x,y)=2y \\ 0<y<1, 0<x<y $$

Now I need to find the marginal PDF of X but how do I select the limits? I am really confused. What is the general method for selection of limits?

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  • $\begingroup$ Hi, welcome. Please add the self-study tag and read its wiki. Here are some hints: 1) Draw $0 < y < 1$ in the $xy$-plane. 2) Draw $x = y$. 3) Where is the $x$-coordinate smaller than $y$-coordinate? $\endgroup$
    – Jim
    Commented Jan 11, 2019 at 16:37
  • $\begingroup$ You don't have to select any limits: they are given to you. We have many questions just like yours, so consider searching our site. Try stats.stackexchange.com/…. Regardless, @Jim's advice to draw a picture is always good to follow. $\endgroup$
    – whuber ♦
    Commented Jan 11, 2019 at 17:22

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