Two cards are drawn at random without replacement from an ordinary deck. Let X be the number of hearts and Y the number of black cards obtained.$($a$)$ Write an expression for the joint pdf$,$f$($x$,$ y$).($b$)$ Tabulate the joint CDF$,$ F$($x$,$ y$).($c$)$ Find the marginal pdf$\text{'}$s$,$f$1($x$)$ andf'$2($y$).($d$)$ Are X and Y independent? $($e$)$ Find PUY $=$ iX $=1].($f$)$ FindP$[$Y$=$yIX$=1].($g$)$ Find P$[$Y$=$yIX$=$x$].($h$)$ TabulateP$[$X Yz$]$;z$=0,1,2.$