Question

Let X represent the number that occurs when a 60 -sided red die is tossed and Y the number that occurs when a 60 -sided green die is tossed.

(a) Find E(X+Y).
E(X+Y) =

Answer 1

The expected value of X+Y is equal to the sum of the expected values of X and Y, which is 61 in this case.

Step-by-step explanation:

The expected value of the sum of two random variables is equal to the sum of their individual expected values. In this case, let's call the number that occurs when the red die is tossed X, and the number that occurs when the green die is tossed Y. The expected value of X+Y is equal to the expected value of X plus the expected value of Y.

Since both dice have 60 sides, the expected value of X and Y is (1+2+3+...+60)/60 = 30.5. Therefore, E(X+Y) = E(X) + E(Y) = 30.5 + 30.5 = 61.