Question

The assets (in billions of dollars) of the four wealthiest people in a particular country are 32,25,20,19. Assume that sample of size n=2 are randomly selected with replacement from this population of four values.

a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sample mean. In the table, values of the sample mean that are the same have been combined

Answer 1

Since all the 16 samples are equally likely so probability of each sample is 1/16 = 0.0625.

Following table shows all the 16 samples and corresponding probabilites:

Samples		x-bar	P(x-bar)
32	32	32	0.0625
32	25	28.5	0.0625
32	20	26	0.0625
32	19	25.5	0.0625
25	32	28.5	0.0625
25	25	25	0.0625
25	20	22.5	0.0625
25	19	22	0.0625
20	32	26	0.0625
20	25	22.5	0.0625
20	20	20	0.0625
20	19	19.5	0.0625
19	32	25.5	0.0625
19	25	22	0.0625
19	20	19.5	0.0625
19	19	19	0.0625

Following table shows the pdf of x-bar:

x-bar	P(x-bar)
19	0.0625
19.5	0.125
20	0.0625
22	0.125
22.5	0.125
25	0.0625
25.5	0.125
26	0.125
28.5	0.125
32	0.0625