1. Let X and Y be random variables with the following joint distribution

a) Fill in the marginal distributions for X and Y. \text { (b) Find } \sigma_{X} \text { and } \sigma_{Y} \text {. } \text { (c) Find } \operatorname{Cov}(X, Y) \text { and } \rho_{X, Y} \text {. } d) Are X and Y independent, why or why not? (e) Find the conditional distribution of X given Y = 0.