# A die is rolled $15$ times. Let $Y$ be the sum of the numbers that comes up. What is the expected value $E(Y)$?

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.

• hint: E(X + Y) = E(X) + E(Y). – Tyler Nov 3 '13 at 14:38

$E[Y] = E[X1 + X2 + X3 + ... + X15] = 15 * E[X] = 15 * \frac{(1+2+3+4+5+6)} 6 = \frac{105} 2$