Refer to Exercise 6.7, in which we found the sampling distribution of the sample median. Is the…

Refer to Exercise 6.7, in which we found the sampling distribution of the sample median. Is the median an unbiased estimator of the population mean μ?

Exercise 6.7

Refer to Exercise 6.5. Assume that a random sample of n = 2 measurements is randomly selected from the population.

a. List the different values that the sample median M may assume, and find the probability of each. Then give the sampling distribution of the sample median.

b. Construct a probability histogram for the sampling distribution of the sample median, and compare it with the probability histogram for the sample mean (Exercise 6.5, part b).

Exercise 6.5

Consider the population described by the probability distribution shown here:

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as follows:

a. Find the sampling distribution of the sample mean .

b. Construct a probability histogram for the sampling distribution of .

c. What is the probability that  is 4.5 or larger?

d. Would you expect to observe a value of  equal to 4.5 or larger? Explain.