# Question

A researcher suspected that the number of between meal snacks eaten by students in a day during final 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.

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.

c. Find and interpret the conditional probability distribution of Y, given that X = 3.

d. Find the covariance between X and Y.

e. Are number of snacks and number of tests independent of each other?

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.

c. Find and interpret the conditional probability distribution of Y, given that X = 3.

d. Find the covariance between X and Y.

e. Are number of snacks and number of tests independent of each other?

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