$(20\%)$Two binary random variables $x$ and $Y$ are distributed according to the

joint distributions:

$P(x=Y=0)=P(x=0,Y=1)=\frac{1}{3},P(x=Y=1)=P(x=1,Y=0)=\frac{1}{6}$

Compute $H(x),H(Y),H(x|Y),H(Y|x),$ and $H(x,Y).$