A die is rolled $15$ times. Let $Y$ be the sum of the numbers that comes up. What is the expected value $E(Y)$?
I know that $15 \leq Y \leq 90$. Then by finding the probability of each of the possible outcome , I can find the $E(Y)$ by using the formula. My question is there any faster method to calculate the probability of each outcome? I find it is very tedious to calculate one by one.