An urn contains exactly three balls numbered 1, 2, and 3, respectively. Random samples of two balls are drawn (first on

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An urn contains exactly three balls numbered 1, 2, and 3,
respectively. Random samples of two balls are drawn (first
one followed by the second) from the urn with replacement.
The average, Xav = 0.5*(X1 + X2) where X1 and X2 are the
numbers on the selected balls, is recorded after each drawing.
Which of the following describes the sampling distribution of
Xav?
Xav
1
1.5
2
2.5
3
Probability
5/9
2/9
1/3
2/9
1
Xav
1
1.5
2
2.5
3
Probability
0
1/3
1/3
1/3
0
Xav
1
1.5
2
2.5
3
Probability
1/10
1/10
1/10
1/10
1/10
Xav
1
1.5
2
2.5
3
Probability
1/9
2/9
1/3
2/9
1/9