Exercise 86 Suppose I have an urn with 9 balls 4 green 3 yel

Exercise 8.6. Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement.

(a) Suppose I draw n times. Let Xn be the number of times I saw a green ball followed by a yellow ball. Calculate the expectation E[Xn].

(b) Let Y be the number of times I drew a green ball before the first white draw. Calculate EY . Can you give an intuitive explanation for your answer?

Exercise 8.12. I roll a fair die four times. Let X be the number of different outcomes that I saw. (For example, if the die rolls are 5,3,6,6 then X = 3 because the different outcomes are 3, 5 and 6.) Find the mean and variance of X.

Solution