I need help with problem 6.5 and 6.14. I want to learn how to solve them.

6.5 Consider the population described by the probability distribution shown here: x 1 2 3 4 5 p (z) 2 32 21 The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as follows: Sample Probability Sample Probability 1 , 1 .04 3, 4 .04 1, 2 06 3, 5 02 1, 3 04 4, 1 04 1, 4 04 4. 2 .06 1, 5 02 14, 3 .04 2, 1 06 4. 4 04 2, 2 09 4. 5 02 2, 3 .06 5, 1 02 2, 4 06 5,2 03 2, 5 03 5,3 02 3, 1 04 5, 4 .02 3, 2 06 5,5 .01 3, 3 04 a. Find the sampling distribution of the sample mean I. b. Construct a probability histogram for the sampling distribution of I. c. What is the probability that I is 4.5 or larger? d. Would you expect to observe a value of I equal to 4.5 or larger? Explain.6.14 Consider the following probability distribution: NW x 4 p(x) a. Find u and o2. b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this distribution. c. Show that x is an unbiased estimator of u. [Hint: Show that E(x) = Exp(x) = M.] d. Find the sampling distribution of the sample variance s2 for a random sample of n = 2 measurements from this distribution. e. Show that s is an unbiased estimator for o