Question 31 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,...

Question 31

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, X_av= 0.5*(X₁ + X₂) where X₁ and X₂
are the numbers on the selected balls, is recorded after each drawing.  Which of the following options correctly describes the sampling distribution of X_av?

Extracted text: Xav 1 1.5 2.5 3 Probability 1/9 2/9 1/3 2/9 1/9 Xav 1 1.5 2 2.5 3 Probability 1/3 1/3 1/3 Xav 1 1.5 2 2.5 3 Probability 1/10 1/10 1/10 1/10 1/10 Хav 1 1.5 2 2.5 3 Probability 5/9 2/9 1/3 2/9 1