Consider the population described by the probability distribution shown below. The random variable is observed twice with independent observations.
X p(x)
1 0.2
2 0.2
3 0.3
4 0.3
Sample 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 Full data set
Probability 0.04 0.04 0.06 0.06 0.04 0.04 0.06 0.06
Sample 3,1 3,2 3,3 3,4 4,1 4,2 4,3 4,4
Probability 0.06 0.06 0.09 0.09 0.06 0.06 0.09 0.09
a. Complete the sampling distribution table. Type the $\bar{x}$ values in ascending order.
$\bar{x}$ 1.5 2 3.5 4
Probability 0.04 0.24 0.21