Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations areindependent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through e below.

x 1 2 3 4 5

p(x) 0.2

0.2 0.4

0.4 0.1

0.1 0.2

0.2 0.1

0.1

x overbar

x 1.0 1.5 2.0 2.5 3 3.5 4 4.5 5

P(

x overbar

x) 0.04

0.04 0.16

0.16 0.2

0.2 0.16

0.16 0.21

0.21 0.12

0.12 0.06

0.06 0.04

0.04 0.01

0.01

Full data set

Sample Mean Probability Sample Mean Probability

1,1 1.0 0.04

0.04 3,4 3.5 0.02

0.02

1,2 1.5 0.08

0.08 3,5 4.0 0.01

0.01

1,3 2.0 0.02

0.02 4,1 2.5 0.04

0.04

1,4 2.5 0.04

0.04 4,2 3.0 0.08

0.08

1,5 3.0 0.02

0.02 4,3 3.5 0.02

0.02

2,1 1.5 0.08

0.08 4,4 4.0 0.04

0.04

2,2 2.0 0.16

0.16 4,5 4.5 0.02

0.02

2,3 2.5 0.04

0.04 5,1 3.0 0.02

0.02

2,4 3.0 0.08

0.08 5,2 3.5 0.04

0.04

2,5 3.5 0.04

0.04 5,3 4.0 0.01

0.01

3,1 2.0 0.02

0.02 5,4 4.5 0.02

0.02

3,2 2.5 0.04

0.04 5,5 5.0 0.01

0.01

3,3 3.0 0.01