Consider the finite population of size N = 3, measurements on the variable x: {2, 3, 4}:
a. derive the population probability distribution for the variable x.
b. compute the population mean and standard deviation
c. Given the above population, sampling with replacement and considering order, how many samples of size n = 2 are possible?
d. derive all samples of n = 2 in the manner as described in c.
e. derive the sampling distribution of the mean as per your results obtained in d.
f. compute the expectation, E(m), or mean of the sampling distribution of the sample mean, m.
g. use the formula for the standard error of the mean
h. Using your result obtained in g, derive for each sample in your population of samples (cf., result obtained in d) a 90% confidence interval.
i. How many of your sample confidence interval cover the true population mean?
j. Does the nominal and actual confidence levels coincide or are they different?