6. Let X1, . .. , X100 be a sample independently drawn from Uniform(0, 1). Let X be the sample mean. (a) Find E[Xi] and Var(X1). (b) Find E[X] and Var(X). (c) Find P(0.45 >2) = 0.05. 8. Suppose we have the following sample drawn independently from a normal distri- bution. 11.8, 9.6, 9.6, 9.2, 10.2 (a) If the population variance is not known, find a 95% confidence interval for the population mean. The sample variance s2 = 1.052 is computed for your conve nience. (b) If we know that the population variance is 1.052, find a 95% confidence interval for the population mean