Consider the following probability distribution:

a. Calculate m for this distribution.

b. Find the sampling distribution of the sample mean x for a random sample of n = 3 measurements from this distribution, and show that x is an unbiased estimator of m.

c. Find the sampling distribution of the sample median M for a random sample of n = 3 measurements from this distribution, and show that the median is a biased estimator of m.

d. If you wanted to use a sample of three measurements from this population to estimate m, which estimator would you use? Why?

Transcribed Image Text:

X 2 4 9 p(x) 1/3 1/3 1/3