Suppose I have an urn with 9 balls 4 green 3 yellow and 2 wh

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?

Solution

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 X

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