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?

Transcribed Image Text:

Number of Tests (X) Number of Snacks (Y) 0.07 0.07 0.06 0.02 0.09 0.06 0.07 0.04 0.06 0.07 0.14 0.16 0.01 0.01 0.03 0.04