## Elementary Statistics (12th Edition)

a) $4.7$ b) Variance, probability: 0, 3/9 0.5, 2/9 8, 2/9 12.5, 2/9 c) $4.7$ d) Yes
a) We know that the average is: $6$. Hence: $σ^2=\frac{Σ(x−\overline{x})^2}{n}=4.7$ b. We know that: $s^2=\frac{n[Σ(f)⋅x^2]−[Σ(f⋅x)^2]}{n(n−1)}$ Hence we can obtain: Variance, probability: 0, 3/9 0.5, 2/9 8, 2/9 12.5, 2/9 c) Using the equation for the mean, we can see that the mean of the above table is $4.7$. d Yes, it is. Finally, we can see that it has the same value as $σ^2$, hence it is an unbiased predictor.