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I hope someone can help me with this!

I have an equation given by: a=b+c which gives me a numerical value for a. b and c are values I plug in.

I also have an equation given by a'=b'+c'. The values of b' and c' have multiple different values with associated probabilities. i.e.; b'=2(50% of time) and b'=3 (25% of time) and b'=5 (25% of time). c'=2(10% of time) and b'=3 (85% of time) and b'=5 (5% of time).

Using R programming I was able to write a script that gives me the probability of a'>a. It uses a stochastic process writing out all possible values for a' and compares it to the value of a. All values where a' is > than a, the probabilities are summed together.

I was wondering how I could write out in mathematical terms what I am doing. I was hoping to include it in a paper I am writing.

Thanks all!

TheFermat
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    I know how to answer your question, but unfortunately the answer is too long to fit in the comment box :) – meh Nov 03 '16 at 02:51
  • Really?! There isn't a simple way of describing the process using a sigma summation symbol? Drat! Any recommendations on how I should describe my process in my paper if it indeed takes up so much text :) – TheFermat Nov 03 '16 at 02:55
  • This question and many generalizations of it are answered in myriad threads on this site: you are asking how to [sum random variables](http://stats.stackexchange.com/search?q=sum+random+variable). Another good term to search on is [convolution](http://stats.stackexchange.com/search?q=convolution), because the sum is computed as the convolution of the distributions. The discussion at http://stats.stackexchange.com/questions/153726 might be a good place to begin. – whuber Nov 03 '16 at 16:55

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