A common component of a risk analysis model is the calculation of the sum of a number of identically distributed random variables, for example: working out how long it will take to serve a number of random customers; or the weight of ten random people getting in an elevator together. In our experience of auditing models, summing random variables is one of the easiest areas to make big mistakes in your model.
The most common problem involves summing a random number of random variables, and we further explain how to sum a number of independent random variables and also how to model the sum of dependent (i.e. correlated) random variables.
Finally, you may be interested in the reverse question of how many random variables add up to a fixed total.