Suppose 250 people out a survey asking how many dogs and cats they own. The results are given in the following table, where the entry in row i and column j is the number of respondents who have exactly i cats and j dogs (e.g. 86 people report having 0 cats and 1 dog)
|
0 |
1 |
2 |
| 0 |
58 |
86 |
14 |
| 1 |
33 |
50 |
9 |
For a person chosen randomly among survey participants, let random variable X be the number of dogs this person owns, and Y be the number of cats this person owns. By dividing the table entries by 250, we obtain a joint PMF for X and Y.
(a) Are X and Y independent?
(b) Find the conditional expected values E(X/Y=1) and E(Y/X=2).