The joint probability mass function of X and Y is given by ,(1, 1) = 0.20, ,(1, 2) = 0.4, ,(2, 1) =0.25, ,(2, 2) = 0.15Find the each of the following. Give exact answers using fraction or decimal.

a. Compute the marginal distribution (), (), =1,2

b. Compute the conditional distribution of X given Y, |(|), =1,2; =1,2

c. Compute the conditional distribution of Y given X, |(|), =1,2; =1,2

d. Are X and Y independent? Why?