A fair red die and a fair blue die are rolled. What is the expected value of the sum of the number on the red die plus three times the number on the blue die?

Name: A fair red die and a fair blue die are rolled. What is the expected value of the sum of the number on the red die plus three times the number on the blue die?
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Question

Quizplus · Accepted Answer

The Answer is Let

X _ { r }

and

X _ { b }

be the random variables for the numbers shown on the dice. We are asked for

E \left( X _ { r } + 3 X _ { b } \right)

. Since these dice are fair, we know that

E \left( X _ { r } \right) = E \left( X _ { b } \right) = ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 3.5

. By linearity of expectation, we have

E \left( X _ { r } + 3 X _ { b } \right) = 3.5 + 3 \cdot 3.5 = 14

.

A Fair Red Die and a Fair Blue Die Are