consider the following probability distribution X 0 1 2 px 1

consider the following probability distribution

X             0         1             2

p(x)         1/3       1/3         1/3

a)find u

b)for a random sample of n=3 observations from the 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 u 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 u and why?

Solution