Cumulative Distribution Functions

Like a fool, I sold my first year statistics textbook and have regretted it ever since. Help a guy out?
It goes like this: I have two random variables, X and Y, for which I know the cumulative distribution functions. I have a third random variable Z, which is just X + Y. Is there a formula calculating the CDF of Z from the CDFs of X and Y?

Your textbook wouldn't have helped you in this case
because there is no such formula... for the generalSorry to contradict you but there is a 'formula' but it is not simple. The text book should have helped.
The Distibution Function (DF) of the sum of two independent random variables is the convolution of the DF's of the two values. So if one differentiates the two CDFs to get the DFs, convolves the result to get the DF of the sum one can then integrate the convolution result to get the CDF of the sum (Wow).
This can be done numerically using several appraches. I have used the Fast Fourier Transform to perform convolution, differentiation and integration but not in this combination. This would be one approach I would consider but it may not be the best.
When I first saw this posted I looked at how one might create the CDF without differentiating the individual CDFs because this step is 'noisy' but I could not find a simple approach. I'm sure there is one but I have not found it.
Using the central limit theorem to obtain an approximation to the PDF is feasable if X and Y have a uni-modal distribution and the variances are similar is size. In the good old days of my using an IBM 360 I used IBM's normal distribution random number generator that just added together 6 samples of a uniform random number generator.

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