The sum of two random variables

In some situations (consider adding some noise to a clean speech signal) the distribution of die sum of two independent random variables, x and y, is required Let 

Pz(z) is required given that Py(y) and px(x) are known (in the same fashion as for PMFs the subscripts on the PDFs have been added to make the distribution clear). From previous results it is easy to obtain 

The expression for the complete PDF of z is required. This may be obtained by convo-Inting the two distributions, 

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What happens if two random variables are added together (Figure A.l) Mean the mean of the sum of two random variables is... 

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