Question

Let x be the number of bicycles owned by families in Canada, for which the probability distribution is as follows:

x 0 1 2 3 ________________________

p(x) .1 .3 .55 .05

a. What is the mean and standard deviation of x?

b. Show the sampling distribution of x̄ for random samples of N=2 measurements drawn from the probability distribution of x.

c.Determine whether or not x̄ is an unbiased estimator of μ

d. An ideal point estimator should be consistent. What does this mean?

Answer 1

d.) An ideal point estimator should be consistent means that the estimator should be unbiased and variance of estimator should tend to 0 for large sample sizes. That means on increasing the sample size, the precision of estimator is maximum.