Question

If you roll a die, you get one of the following numbers: 1, 2, 3, 4,...

If you roll a die, you get one of the following numbers: 1, 2, 3, 4, 5, 6. Each possibility occurs with equal probability of 1/6. The expected value of a dice roll is E(D)= 3.5 and the variance of a dice roll is Var(X) = 2.917.

a) Suppose you roll a die and then add 1 to the roll to get a new random variable taking one of the following numbers: 2,3,4,5,6,7. What is the variance of this new random variable?

b) Suppose you roll a die and then multiply the roll by 2 to get a new random variable taking one of the following numbers: 2, 4, 6, 8, 10, 12. What is the variance of this new random variable?

c) Suppose you roll two dice and then take the sum of the two dice to get a number between 2 and 12. What is the variance of this sum random variable?

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