Do my assignment

Solution:
To find conditional prob mass function of X given that Y =3
i.e. when 3 black balls are drawn out of 6 balls other three are left.
Now let us calculate no of white and red balls. We need not consider black as 3 black is given
Now we are to draw 3 remaining balls from remaining
3 W and 6 R balls
X = no of white balls can take values as 0,1,2,3
P(X=r) = Prob of drawing r white balls from 3 w and 6 R balls, r =0,1,2,3
=
Thus distribution of X would be got by substituting r =0,1,2,3
    x
    P
     
     
    0
    0.238095
    1
    0.535714
    2
    0.214286
    3
    0.011905
     
    1
When y=1, we have distribution function of X as prob of drawing no of white balls for the remaining 5 balls from 3W and 6R
    x
    P
    x*p
     
     
     
    0
    0.047619
    0
    1
    0.357143
    0.357143
    2
    0.47619
    0.952381
    3
    0.119048
    0.357143
     
    1
    1.666667
E(X/y=1) = total...