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This question already has an answer here:

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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marked as duplicate by whuber probability Jan 11 at 17:23

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ 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 Jan 11 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 Jan 11 at 17:22