# Question: Consider the following probability distribution a Find b For a

Consider the following probability distribution:

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?

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?

**View Solution:**## Answer to relevant Questions

Refer to Exercise 6.5. a. Show that x is an unbiased estimator of μ. b. Find σ2x-bar. c. Find the probability that x-bar will fall within 2σ x-bar of μ. A random sample of n = 100 observations is selected from a population with μ = 30 and σ = 16. a. Find μx-bar and σx-bar. b. Describe the shape of the sampling distribution of x-bar. c. Find P(x-bar ≥ 28). d. Find ...Refer to the Applied Psychology in Criminal Justice (Sept. 2009) investigation of the personality characteristics of drug dealers, Exercise. Convicted drug dealers were scored on the Wanting Recognition (WR) Scale—a scale ...Interpersonal violence (e.g., rape) generally leads to psychological stress for the victim. Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the relationship between ...What is the confidence level of each of the following confidence intervals for µ? a. ± 1.96(σ/√n) b. ± 1.96(σ/√n) c. ± 1.96(σ/√n) d. ± 1.96(σ/√n) e. ± 1.96(σ/√n)Post your question