18) A researcher suspected that the number of between-meal snacks eaten by students in a day during nal examinations 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 Number of Tests Snacks (Y) 0 1 2 a. Find the probability distribution of X and compute the mean number of tests taken by students on that day. b. Find the probability distribution of Y and, hence, the mean number of snacks eaten by students on that day. Find and interpret the conditional probability distribution of Y, given that X = 3. (1. Find the covariance between X and Y. e. Are number of snacks and number of tests independent of each other? 9