jmc

Question

A fair 6-sided die is rolled. If I roll n, then I win n^2 dollars. What is the expected value of my win? Express your answer as a dollar value rounded to the nearest cent.

Accepted Answer

Each number from 1 to 6 has probability 16 of being rolled, so the expected value is align* E &= (16 1^2) + (16 2^2) + + (16 6^2) &= 16(1 + 4 + 9 + 16 + 25 + 36) &= 916 & $15.17. align*