Math 5010-2 Name:
Quiz 7
10/29/08
1. Six balls, labeled A, B, C, D, E, F, are in an urn. Two are selected
successively at random with the first one replaced before the second is drawn.
Let Xbe the number of times ball A is chosen and Ythe number of times ball
B or C is chosen. Obviously, 0 ≤X≤2 and 0 ≤Y≤2.
(a) Give the joint probability mass function of Xand Yin the form of a
table, with rows corresponding to xvalues (increasing from top to bottom) and
columns corresponding to yvalues (increasing from left to right). If correct, the
entries will sum to 1.
Table 1: Joint distribution.
x/y 0 1 2 totals
0 (3/6)22(2/6)(3/6) (2/6)2
1 2(1/6)(3/6) 2(1/6)(2/6) 0
2 (1/6)20 0
totals
(b) Find the marginal probability mass functions of Xand of Y, and be sure
to indicate which is which.
Table 2: Joint distribution with marginals. Marginal of Xis in right column,
that of Yis in bottom row.
x/y 0 1 2 totals
0 9/36 12/36 4/36 25/36
1 6/36 4/36 0 10/36
2 1/36 0 0 1/36
totals 16/36 16/36 4/36
(c) Are Xand Yindependent? Justify your answer.
No. For example 0 = P(X= 2, Y = 2) 6=P(X= 2)P(Y= 2) = 4/(36)2.
1