$1.$ Consider the $2-$d probability distribution:P$($x$,$y$)=$ alpha$*$xyx $\backslash$in $\backslash \{1,2,3\backslash \}$ y $\backslash$in $\backslash \{1,2,3,4\backslash \},$alpha $\backslash$in Ra$)$ Given the domain of X and Y$,$ what number must a be if this is to define a probability distribution?b$)$ Find the marginal distribution of X $($use the law of total probability$).$c$)$ Find the marginal distribution of Y$.$d$)$ Find the conditional distribution of Y given Xe$)$ What is the correlation of X and Y$?$