by Stat_learner12   Last Updated June 12, 2019 08:19 AM

X and Y are independent and identically distributed uniform (0,1) random variables. Find E(X|X>Y) Please explain it step by step. I am getting ans 0.5 while the actual answer given is 0.66

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A simple graphical approach is via using just x-y plane. These variables are independent, so their joint is defined over the square $$[0,1]\times[0,1]$$. This region shows us all possible pairs of $$(X,Y)$$ When $$X>Y$$ is given as event, we should focus on the region below the line $$X=Y$$, where it contains $$(X,Y)$$ pairs having the desired ordering. So, your interested region is a triangle with corners $$\{(0,0),(1,0),(1,1)\}$$. What is the center of mass of this triangle, and what is its x coordinate?