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papak Group Title

Can anyone help me with the following please? I have a question regarding Laplace Transformation (LT) . But its application in probability theory. I want to use LT to find the density of random variables Z = X + Y where X and Y are iid Uniform (0,1). I know the density of Z is convolution of density of X and Y So if i find the LT of density of X which is 1/s then 1/ s^2 is LT of density of Z so by inverse LT the density of Z should be t. This seems correct for 0<Z<1 but what am I missing that I cannot find the density of Z when 1<Z<2?

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