# Probability and Statistics

## Let X1, . , . , X7 be a random sample from the normal model with mean μ variance σ2-1. Consider the following two estimators of μ 5 and 7 2 Is either estimator unbiased?

Let X1, . , . , X7 be a random sample from the normal model with mean μ variance σ2-1. Consider the following two estimators of μ 5 and 7 2 Is either estimator unbiased? EXPERT ANSWER

## I. Let Xi, ,X, denote a random sample from a population with mean μ and variance σ2 Assume n 2. Consider the following two estimators (W, and Vo) for μ: (X1 + X2) 2 1-1 Find the relative efficiency of the second estimator compared to the first. Which estimator would you prefer based on this and why? 2. Find E(S2) and Var(S2) when X1, X2,… , Xn is a random sample from a normal distribution with mhean μ ad variance σ2. Is S2 a consistent estimate of σ2?

Let X1, . . . , Xn denote a random sample from a population with mean µ and variance σ 2 . Assume n > 2. Consider the following two estimators (Wn and Vn) for µ: EXPERT ANSWER

## The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the 99% lower confidence bound on the mean strength?

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the 99% lower confidence bound on the mean strength? EXPERT ANSWER Confidence interval for Population mean is given as …

## The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the sample mean of this data set?

The compressive strength of concrete is tested by a civil engineer who tests 12 specimen and obtains the follow data, in psi: 2216, 2225, 2318, 2237, 2301, 2255, 2249, 2281, 2275, 2204, 2263, 2295. What is the sample mean of this data set? EXPERT ANSWER