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

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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

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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