# Writing an equation

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!

• I know how to answer your question, but unfortunately the answer is too long to fit in the comment box :)
– meh
Nov 3 '16 at 2:51
• 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 :) Nov 3 '16 at 2:55
• This question and many generalizations of it are answered in myriad threads on this site: you are asking how to sum random variables. Another good term to search on is convolution, because the sum is computed as the convolution of the distributions. The discussion at stats.stackexchange.com/questions/153726 might be a good place to begin.
– whuber
Nov 3 '16 at 16:55