, . aqua ikeiy. } Find the mean variance, and standard deviation of the populathn. a , b) List all the samples of size 2 chosen with replacement, cl Construct the sampling distribution for the samples in part b. :0 Find the mean of the sampling distribution, In: , and the variance of the sampling distribution, oz: . e] How do the mean and variance of the sampling distribution compare to the mean and variance ofthe population? population. How many samples of size 3 are there in the sampling ' ' ' distribution? The variance? W87-02: Consider the following probability distribution. X 3 7 p(x) 0.75 0.25 a) Find the sampling distribution for & and & for random samples of size n = 3 measurements taken with replacement from this distribution by listing all possible values of & and & , and find the probabilities of each. b) Find u for the original distribution. c) Using the data from Part a, calculate /, and up . d) Which of these is an unbiased estimator of u (if any) and which is a biased estimator of u (if any)?c) Find the method of moments estimator for 0. d) Find the method of moments estimate for 0 based on the data: 0.5, 0.3, 0.1, 0.1, and 0.2 e) Find the maximum likelihood estimator for 0. 1) Using the data from Part d, find the maximum likelihood estimate for 0. W87-06: Let X1, Xz Xs. ...; Xn be a random sample of size n from a geometric distribution with parameter p. a) Find the method of moments estimator for p.b) Find the maximum likelihood estimator for p. c) Find the point estimate for p using the data: 2, 1, 1, 1, 1, 6, 1, 5 WB7-07: Let X1, Xx Xx ..., Xn be a random sample of size n from a normal distribution with X"Normal(H, 3). a) Find the maximum likelihood estimator for J. b) Using the following sample data, find the point estimate for u. 14 6 12 3 5 12 1 15 6 8