Suppose you have a 5-sided die in which each face is equally likely to come up. It has values {1,2,3,4,5}. The die is rolled once. Let X be the number facing up. Find the variance of X. Variance of a set of n equally likely values: Var (X) = , 21=1(*; -#) , where u is the expected value of X. Select one: O a. 2 O b. 2 O c. 10 O d. 3 Suppose are studying the distribution of a random variable X. You have collected a sample of 25 observations (n=25) and calculated the sample mean, X, to be 6. You also know that the standard error of the sample mean is s. e. = 2. You wish to test the following hypothesis about the population mean, H: Ho:H = 1 Hip # 1 Which of the following gives a 95% confidence interval of the population mean? Do you reject Ho? Select one: O a. (6- 1.96 * 2, 6 + 1.96 * 2). Yes, reject Ho. b. (6 - 1.96 * 2, 6 + 1.96 * 2). No, do not reject Ho. O c. (6- 2.064 * 2, 6 + 2.064 * 2). Yes, reject Ho. O d. (6-2.064 * 2, 6 + 2.064 * 2). No, do not reject Ho