Let X,Y~U(0,1) independent (which means that they are distributed uniformly on [0,1]). find the distribution of U=X-Y.(adsbygoogle = window.adsbygoogle || []).push({});

well intuitively U~U(-1,1), but how to calculate it using convolution.

I mean the densities are f_Z(z)=1 for z in [-1,0] where Z=-Y and f_X(x)=1 for x in [0,1], now i want to calculate using convolution i.e:

[tex]f_U(u)=\int_{-\infty}^{\infty}f_X(t)f_Z(u-t)dt[/tex]

where t in [0,1] and u-t in [-1,0] so u is in [-1,1], as i said i know what intuitively it should be but i want to formally calculate it, i.e compute the integral, and t is between [u,u+1], but i think that this integral doesnt apply for a difference between random variables, any tips?

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# Computing distributions by using convolution.

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