An urn contains one black ball and three white balls. Four balls are drawn from the urn.Let ik = 1 if the outcome of the kth draw is black and ik = 0 if the outcome of the kth ballis white. Define the three random variables:X = i1+i2+ i3+i4;
Y = min i1; i2; i3; i4;Z = max i1; i2; i3;i4;
W =i1:(a) Find the probability law for (X; Y;Z) if each ball is put back into the urn after each
draw.(b) Find the probability law for (X; Y;Z) if each ball is not put back into the urn aftereach draw.
(c) Find the conditional probability laws for every variable in (X; Y;Z) given the possible
value

Question

An urn contains one black ball and three white balls. Four balls are drawn from the urn.Let ik = 1 if the outcome of the kth draw is black and ik = 0 if the outcome of the kth ballis white. Define the three random variables:X = i1+i2+ i3+i4;
Y = min i1; i2; i3; i4;Z = max i1; i2; i3;i4;
W =i1:(a) Find the probability law for (X; Y;Z) if each ball is put back into the urn after each
draw.(b) Find the probability law for (X; Y;Z) if each ball is not put back into the urn aftereach draw.
(c) Find the conditional probability laws for every variable in (X; Y;Z) given the possible
value