Problem 1 Let X1, ..., X40 be independent and identically distributed copies of random variables X...

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Problem 1 Let X1, ..., X40 be independent and identically distributed copies of random variables X generated from a computer routine. Let p = P((X 1) < 30) (1) a) Give the point estimate and 95 percent confidence interval of p if, among all the values of the Xi, 2 appeared 11 times, 4 appeared 5 times, 5 appeared 10 times, 6 appeared 2 times, 8 appeared 7 times, 9 appeared 4 times and 24 appeared 1 times. b) Repeat part a) except using calculated sample variance S2 instead of the relationship between mean and variance for Bernoulli distribution (i.e. Var= p(1 - p)) to construct the confidence interval. Problem 1 Let X1, ..., X40 be independent and identically distributed copies of random variables X generated from a computer routine. Let p = P((X 1) < 30) (1) a) Give the point estimate and 95 percent confidence interval of p if, among all the values of the Xi, 2 appeared 11 times, 4 appeared 5 times, 5 appeared 10 times, 6 appeared 2 times, 8 appeared 7 times, 9 appeared 4 times and 24 appeared 1 times. b) Repeat part a) except using calculated sample variance S2 instead of the relationship between mean and variance for Bernoulli distribution (i.e. Var= p(1 - p)) to construct the confidence interval.