A researcher suspected that the number of between-meals snacks eaten by students in a day during final examinations week might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey. NUMBER OF TESTS (N) NUMBER OF SNACKS (Y) 0 2 0219 2 3 5688 07 09 .06 .02 9388 06 38 06 07 99 .01 07 14 .03 04 .16 04

(a) Find the probability function of X and hence the mean number of tests taken by students on that day.

(b) Find the probability function of Y and hence the mean number of snacks eaten by students on that day.

(c) Find, and interpret, the conditional probability function of Y. given X-3.

(d) Find the covariance between X and Y.

(e) Are number of snacks and number of tests independent of each other?