Consider a ferry that can carry both buses and cars across a waterway. Let X and Y denote the number of buses and cars, respectively, carried on a given trip. The joint PMF for X and Y is given by

x

y 0 1 2

0 0.01 0.01 0.03

1 0.03 0.08 0.07

2 0.03 0.06 0.06

3 0.07 0.07 0.13

4 0.12 0.04 0.03

5 0.08 0.06 0.02

- (a) Give the marginal PMFs of X and Y .
- (b) Find the expected value and the standard deviation of X.
- (c) Find the expected value and the standard deviation of Y .
- (d) Give the conditional distribution of X given Y = 2.
- (e) Find E[X|Y = 2].
- (f) If the ferry carries only 1 bus across the waterway on a given trip, what is the
- expected number of cars carried on the same trip?
- (g) Are X and Y independent? Give reason.
- (h) Find corr(X, Y ).

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