This is something of a semantic question. Studying for CFA and expected value formula is presented as a kind of "weighted average" for a range of expected monetary outcomes.
The formula is written thusly: E(X) = ΣX * P(X)
So, we sum the products of each variable by it's attendant probability. However, we don't then divide that sum by the total of data points. Can anyone explain why this formula is presented as a "weighted average" if no division is taking place after adding up our weighted outcomes?
You would divide by the sum of the weights, which is 1 in this case, because $\sum_X P(X)=1$.