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If $X$ and $Y$ are independent and both follows $\operatorname{Uniform}(0,1)$. Find $P(|X-Y|)\ge1/2)$

Here we are given the difference of $2$ uniform variates...But I think the density difference of $2$ uniform variates is of no use here.

Here we get two equation from definition of modules.When I plot graph of the two I get two triangles then I simply sum the areas and subtract it by $1$ and get $\frac34$....But the ans. does not match.....What's the problem??

Siong Thye Goh
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demon
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The error is you should not subtract it by $1$.

You just have to find the corresponding area of the two triangle and divide it by the area of the whole domain which happens to be $1$.

Hence you just have to sum up the area of the two triangles.

Siong Thye Goh
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