1 What Is Statistics 2 Probability 3 Discrete Random Variables And Their Probability Distributions 4 Continuous Variables And Their Probability Distributions 5 Multivariate Probability Distributions 6 Functions Of Random Variables 7 Sampling Distributions And The Central Limit Theorem 8 Estimation 9 Properties Of Point Estimators And Methods Of Estimation 10 Hypothesis Testing 11 Linear Models And Estimation By Least Squares 12 Considerations In Designing Experiments 13 The Analysis Of Variance 14 Analysis Of Categorical Data 15 Nonparametric Statistics 16 Introduction To Bayesian Methods For Inference expand_more
8.1 Introduction 8.2 The Bias And Mean Square Error Of Point Estimators 8.3 Some Common Unbiased Point Estimators 8.4 Evaluating The Goodness Of A Point Estimator 8.5 Confidence Intervals 8.6 Large-sample Confidence Intervals 8.7 Selecting The Sample Size 8.8 Small-sample Confidence Intervals For μ And Μ1 − Μ2 8.9 Confidence Intervals For σ 2 8.10 Summary Chapter Questions expand_more
Problem 1E: Using the identity ()=[E()]+[E()]=[E()]+B(), Show that MSE()=E[()2]=V()+(B())2. Problem 2E: a. If is an unbiased estimator for , what is B()? b. If B()=5, what is E()? Problem 3E: Suppose that is an estimator for a parameter and E()=a+b for some nonzero constants a and b. a. In... Problem 4E: Refer to Exercise 8.1. a. If is an unbiased estimator for , how does MSE () compare to V()? b. If ... Problem 5E: Refer to Exercises 8.1 and consider the unbiased estimator that you proposed in Exercise 8.3. a... Problem 6E: Suppose that E(1)=E(2)=, V(1)=12, and V(2)=22. Consider the estimator 3=a1+(1a)2. a. Show that 3 is... Problem 7E: Consider the situation described in Exercise 8.6. How should the constant a be chosen to minimize... Problem 8E: Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution with density... Problem 9E: Suppose that Y1, Y2,, Yn constitute a random sample from a population with probability density... Problem 10E: The number of breakdowns per week for a type of minicomputer is a random variable Y with a Poisson... Problem 11E: Let Y1, Y2, , Yn denote a random sample of size n from a population with mean 3. Assume that 2 is... Problem 12E: The reading on a voltage meter connected to a test circuit is uniformly distributed over the... Problem 13E: We have seen that if Y has a binomial distribution with parameters n and p, then Y/n is an unbiased... Problem 14E Problem 15E: Let Y, Y2,,Yn denote a random sample of size n from a population whose density is given by... Problem 16E: Suppose that Y1, Y2,,Yn constitute a random sample from a normal distribution with parameters and... Problem 17E: If Y has a binomial distribution with parameters n and p, then p1=Y/n is an unbiased estimator of p.... Problem 18E: Let Y1, Y2, , Yn denote a random sample of size n from a population with a uniform distribution on... Problem 19E Problem 20E: Suppose that Y1, Y2, Y3, Y4 denote a random sample of size 4 from a population with an exponential... format_list_bulleted
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