NW 5.10 Consider the following probability distribution: X p(x) 0 colme 1 موا مع 2 -1/32 a. Find μ. b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean. c. Find the sampling distribution of the median of a sample of n = 3 observations from this population.

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NW 5.10 Consider the following probability distribution:
X
p(x)
0
1102
3
1
33
2
퓸
a. Find μ.
b. For a random sample of n = 3 observations from this distribution,
find the sampling distribution of the sample mean.
c. Find the sampling distribution of the median of a sample of n = 3
observations from this population.
d. Refer to parts b and c, and show that both the mean and median
are unbiased estimators of μ for this population.
e. Find the variances of the sampling distributions of the sample
mean and the sample median.
f. Which estimator would you use to estimate μ? Why?
Transcribed Image Text:NW 5.10 Consider the following probability distribution: X p(x) 0 1102 3 1 33 2 퓸 a. Find μ. b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean. c. Find the sampling distribution of the median of a sample of n = 3 observations from this population. d. Refer to parts b and c, and show that both the mean and median are unbiased estimators of μ for this population. e. Find the variances of the sampling distributions of the sample mean and the sample median. f. Which estimator would you use to estimate μ? Why?
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