Hey I would like to have this question answered neatly. Thanks :)

Question 1. (3+3+3.5+1.5 points) The joint distribution P(X = 3:, Y = y) of random variables X and Y is displayed in the following table. a): Find the marginal distribution of X. b): Find the mean and variance of X (Note that Y has the same mean and variance). 0): Find the correlation p(X, Y). Is there any linear relationship between X and Y? Comment. d): Find the distribution table for P(Y = yIX = 0)