$1.$ Suppose from a deck of card, $4$ cards are drawn at random, Let X be the number of king obtained,

and Y the number of heart cards obtained.

a$.$ Obtain the joint probability distribution of $($X$,$Y$)!$

b$.$ Find the marginal distribution of X$,$ and Y$,$ respectively!

c$.$ Find the expected value of X and Y$!$

d$.$ Is X and Y independent?