1) I assume n=N
2) are we replacing the balls after we select them?
you need to find the joint distribution of X and Y
There are 2*N balls inside a jug. N of them black and n are white.
call I(1)=0 if the first ball we took out is black
I(1)=1 if the first ball we took out is white
same for I(2),
I(2)=1 if the second ball we took out is white
I(2)=0 if the second ball taken out is black
now X=I(1)
Y=I(1)+I(2)
compute E(Var(Y|X))
E stands for expectancy
Var stands for Variance
thanks for your help!