In this exercise, you are to consider two variables, x and y, defined on a hypothetical population. Following are the conditional distributions of the variable y corresponding to each value of the variable x.

y x

A B C Total 0 0.316 0.316 0.316 1 0.422 0.422 0.422 2 0.211 0.211 0.211 3 0.047 0.047 0.047 4 0.004 0.004 0.004 Total 1.000 1.000 1.000

a. Are the variables x and y associated? Explain your answer.

b. Determine the marginal distribution of y.

c. Can you determine the marginal distribution of x? Explain your answer.