Answer
a) $2.16$
b) Sample;$σ$
(4,4); 0
(5,5); 0
(9,9); 0
(4,5); 0.71
(4,9); 3.536
(5,4); 0.71
(5,9); 2.828
(9,4); 3.5356
(9,5); 2.828
c) $1.572$
d) No
Work Step by Step
a) We know that for the standard deviation: $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}=2.16$
b) There are $9$ possibilities, because there are $3$ numbers that can go into $9$ different pairs of two ($3^2=9$).
$σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}.$ Each sample has a probability of $1/9$. Hence we find:
Sample;$σ$
(4,4); 0
(5,5); 0
(9,9); 0
(4,5); 0.71
(4,9); 3.536
(5,4); 0.71
(5,9); 2.828
(9,4); 3.5356
(9,5); 2.828
c) Since the probabilities are equal, we can use the normal equation for mean. Hence the mean is $1.572$.
d) Since the results of part a) and part c) are not equal, we can see that the sampling median is not an unbiased predictor.
