Question: You roll a 4-sided die with sides numbered from 1 to 4. If the outcome is a 1, you get 1 dollar, roll again. is

You roll a 4-sided die with sides numbered from 1 to 4. If the outcome

is a 1, you get 1 dollar, roll again.

is a 2, you get 2 dollars, roll again.

is a 3, you get 3 dollars, roll again.

is a 4, you stop rolling.

Let X be the number of times you roll the die. Let Y be the amount of money you win.

(1) Is E[X] 4?

(2) Is E[Y] 6?

Why?

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