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TOPIC

TEXT BY MILLER & MILLER

HOMEWORKS

CHAPTER 1. INTRODUCTION

Counting Techniques

§ 1.1-1.3

Pg. 17-24

1.6, 1.7, 1.24, 1.25, 1.28, 1.31, 1.34, 1.35, 1.36, 1.40, 1.43, 1.49, 1.53, 1.54

 

CHAPTER 2. PROBABILITY

Introduction & Sample Space and Events

§ 2.1, 2.2, 2.3

Pg. 32-36

2.4, 2.6, 2.10, 2.12, 2.14, 2.20, 2.22

 

 

Probabilities &

Rules of Probability

§ 2.4-2.5

Pg. 46-52

2.25, 2.27, 2.31, 2.33, 2.34, 2.36, 2.39, 2.42, 2.47, 2.53, 2.55, 2.56

 

 

Conditional Probabilities

§ 2.6

Pg. 65-72

2.64, 2.69, 2.75, 2.76, 2.83, 2.88, 2.91, 2.98, 2.99, 2.104

Independent Events

§ 2.7

Bayes' Formula

§ 2.8

CHAPTER 3. PROBABILITY DISTRIBUTIONS & DENSITIES

Random Variables

§ 3.1

Pg. 86-89

3.2, 3.4, 3.11, 3.12, 3.20, 3.21

Discrete Random Variables

§ 3.2

Continuous Random Variables

§ 3.3-3.4

Pg. 97-101

3.37, 3.38, 3.40, 3.41, 3.51, 3.53, 3.55

Multivariate Distributions (Jointly Distributed Random Variables)

§ 3.5

Pg. 111-115

3.56, 3.57, 3.63, 3.76. 3.77, 3.85, 3.87

Marginal & Conditional Distributions

§ 3.6, 3.7

Pg. 125-128

3.89, 3.90, 3.94, 3.105, 3.108

TOPIC

TEXT BY MILLER & MILLER

HOMEWORKS

CHAPTER 4. EXPECTATION

Expectation of a Random Variable, Moments, Chebyshev's Theorem

§ 4.1, 4.2, 4.3, 4.4

Pg. 137-140

4.6, 4.8, 4.9, 4.19, 4.20

Pg. 149-153

4.27, 4.34, 4.39, 4.43, 4.48, 4.54

Moment Generating Functions

Product Moments

Moments of Linear Combinations

§ 4.5, 4.6, 4.7

Pg. 163-166

4.64, 4.65, 4.69, 4.78, 4.80

Conditional Expectation

§ 4.8

CHAPTER 5. DISCRETE PROBABILITY DISTRIBUTIONS

Introduction & Discrete Uniform

§ 5.1, 5.2

Pg. 175-180

5.5, 5.16, 5.19, 5.26, 5.27

Bernoulli & Binomial

§ 5.3, 5.4

Negative Binomial & Geometric

§ 5.5

Pg. 192-198

5.39, 5.46, 5.55, 5.58, 5.61, 5.72, 5.78

Hypergeometric

§ 5.6

Poisson

§ 5.7

Multinomial

§ 5.8

Pg. 201-202

5.84, 5.87

Multivariate Hypergeometric

§ 5.9

CHAPTER 6. CONTINUOUS PROBABILTY DISTRIBUTIONS

Introduction & Uniform

§ 6.1, 6.2

Pg. 211-216

6.1, 6.15, 6.32, 6.34, 6.39, 6.41

Gamma Family

§ 6.3

Beta

§ 6.4

Normal

§ 6.5

Pg. 225-229

6.49, 6.58, 6.63, 6.65, 6.70, 6.72

Normal Approximations

§ 6.6

Bivariate Normal

§ 6.7

Pg. 233-234

6.76, 6.82, 6.83

CHAPTER 7. FUNCTIONS OF RANDOM VARIABLES

Introduction & Distribution Function Techniques

§ 7.1, 7.2

Pg. 239-241

7.1, 7.8, 7.12, 7.13

Transformation Technique (one variable)

§ 7.3

Pg. 256-261

7.16, 7.24, 7.30, 7.38, 7.49

Transformation Technique (several variables)

§ 7.4

Moment Generating Function Technique

§ 7.5

Pg. 263-265

7.57, 7.61, 7.64, 7.67

CHAPTER 8. SAMPLING DISTRIBUTIONS

Introduction & Sample Mean

§ 8.1, 8.2

Pg. 275-279

8.2, 8.4, 8.5, 8.18, 8.19, 8.24, 8.27, 8.34

 

Sample Mean (Finite Populations)

§ 8.3

Chi-Square

§ 8.4

Pg. 289-293

8.39, 8.40, 8.41, 8.55, 8.61, 8.64, 8.65,

t

§ 8.5

F

§ 8.6

Order Statistics

§ 8.7

Pg. 296-298

8.75, 8.87

CHAPTER 9. DECISION THEORY

Introduction & Theory of Games

§ 9.1, 9.2

Pg. 308-312

9.4, 9.8, 9.11, 9.13, 9.15, 9.16

Statistical Games

§ 9.3

Pg. 319-321

9.22, 9.24, 9.27

Decision Criteria

§ 9.4

Minimax Criterion

§ 9.5

Bayes Criterion

§ 9.6

CHAPTER 10. ESTIMATION: THEORY

Introduction & Unbiasedness

§ 10.1, 10.2

Pg. 330-334

10.1, 10.7, 10.16, 10.23, 10.32, 10.34

Efficiency

§ 10.3

Consistency

§ 10.4

Pg. 342-343

10.38, 10.39, 10.45, 10.46, 10.47, 10.51

Sufficiency

§ 10.5

Robustness

§ 10.6

Method of Moments

§ 10.7

Pg. 349-352

10.55, 10.58, 10.64, 10.66, 10.74, 10.80, 10.87

Method of Maximum Likelihood

§ 10.8

Bayesian Estimation

§ 10.9

Pg. 358-359

10.92, 10.97

CHAPTER 11. ESTIMATION: APPLICATIONS

Introduction & Mean

§ 11.1, 11.2

Pg. 368-372

11.2, 11.5, 11.11, 11.16, 11.19, 11.26, 11.27

Difference Between Means

§ 11.3

Proportions

§ 11.4

Pg. 376-378

11.29, 11.30, 11.35, 11.36, 11.40, 11.44, 11.47, 11.49

Difference Between Proportions

§ 11.5

Variance

§ 11.6

Pg. 380-381

11.52, 11.56, 11.59

Ratio of Two Variances

§ 11.7

Use of Computers

§ 11.8

CHAPTER 12. HYPOTHESIS TESTING: THEORY

Intro. & Statistical Hypothesis

§ 12.1, 12.2

Pg. 392-396

12.1, 12.3, 12.8, 12.12, 12.18, 12.22, 12.24, 12.25

Losses & Risks

§ 12.3

Neyman-Pearson Lemma

§ 12.4

Power Function

§ 12.5

Pg. 405-409

12.28, 12.32, 12.33, 12.40, 12.43, 12.44

Likelihood Ratio Test

§ 12.6

CHAPTER 13. HYPOTHESIS TESTING: APPLICATIONS

Introduction & Means

§ 13.1, 13.2

Pg. 421-425

13.2, 13.7, 13.11, 13.14, 13.20, 13.25, 13.29, 13.30

Difference Between Means

§ 13.3

Variance

§ 13.4

Pg. 429

13.36, 13.44

Proportions

§ 13.5

Pg. 435-437

13.45, 13.51, 13.54, 13.55, 13.63, 13.69

Differences Among k Proportions

§ 13.6

Contingency Tables

§ 13.7

Pg. 443-446

13.75, 13.78, 13.81, 13.82

Goodness of Fit

§ 13.8

Use of Computers

§ 13.9

CHAPTER 14. REGRESSION AND CORRELATION

TBA

CHAPTER 15. ANALYSIS OF VARIANCE

TBA

CHAPTER 16. NONPARAMETRIC TESTS

TBA

 

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