1. A researcher suspected that the number of between meals snacks eaten by students in a day during final examinations might depend on the number of tests a students had to take on that day. The accompanying table shows joint probabilities, estimated from a survey

Number of tests (X)

Number of snacks(Y)

0

1

2

3

0

0.07

0.09

0.06

0.01

1

0.07

0.06

0.07

0.01

2

0.06

0.07

0.14

0.03

3

0.02

0.04

0.16

0.04

a. Find the probability distribution of X and compute the mean number of test taken by students on that day

b. Find the probability distribution of Y and compute the mean number of snacks 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?