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The random variables X and Y are independent, each with the uniform distribution on [−1, 1].

Find: $$P[max (X,Y) >0.5]$$ Apparently there is an easy approach without integration, but I am having trouble visualizing it. Thoughts?

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possible duplicate of Expected value of max(x, y) – kaine Nov 10 '13 at 20:34

1 Answer 1

Draw the square $[-1,1]\times[-1,1]$. Shade in the region where $X$ or $Y$ is greater than $0.5$. Calculate the proportion of the shaded area to the area of the square.

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