0
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ hint: E(X + Y) = E(X) + E(Y). $\endgroup$ – Tyler Nov 3 '13 at 14:38
5
$\begingroup$

Let X be the random variable came from one roll.

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.