If X and Y have the joint density function

fXY $($x$,$ y$)=3/4+$ xy; $0<$ x $<1,0<$ y $<1$

a$)$ fY$|$X $($y$|$x$),$

b$)$ P $($ Y $>1/2|0<$ X $<(1)/(2))$

c$)$ Are X and Y independent? Show.

d$)$ Calculate the correlation between X and Y$.$