An urn contains contains 5 balls: 3 green, 1 yellow and 1 white ones. We draw a ball from the urn repeatedly with replacement until we see the first green or yellow ball, and then we stop. Let X denote the number of draws we needed. Let Y equal to 1 if the last draw is green and 2 if the last draw is yellow.

1. Find the joint distribution of (X, Y ). You can leave your results with combination terms. Hint: consider Y = 1 and Y = 2 separately. 2. Find the marginal mass function of X.

3. Find the marginal mass function of Y .

4. X and Y independent?