Reading

I will not give a list of the form read section x by day y. I will present below a useful order in which to read the material. BPT is the book by Ash, MSA is the book by Mendenhall et al, and PSE is Probability and Statistics for Engineers by Miller and Freund, on reserve at the library. When readings from several books are given, the first book listed should be regarded as the primary source. Not all the reading will be discussed in class, particularly sections that are simply calculations using elementary calculus and algebra. If you have questions on anything you read, please ask!

1.

Introduction:

(a)

Statistics. Chapter 1 of MSA.

(b)

Probability. Chapter 1.1 of BPT. Chapter 2.1 and 2.2 of MSA.

2.

Basic Concepts of Probability

(a)

Algebra of Events. Chapter 1.2 of BPT. Chapter 2.3 and 2.4 of MSA.

(b)

Measuring Probability. Chapter 1.3 of BPT. Chapter 2.5 of MSA. Pages 51 and 52 of MSA. Chapter 2.12 of MSA.

(c)

How to Count Efficiently. Chapter 1.4, 1.6 and 1.7 of BPT. Chapter 2.6 of MSA.

(d)

Independence and Conditional Probability. Chapter 1.5 and 1.6 of BPT. Chapter 2.7 of MSA. Page 50 of MSA. Chapter 2.9 and 2.10 of MSA.

3.

Random Variables.

(a)

Quantifying outcomes of experiments. Chapter 2.1 and 2.2 of BPT. Chapter 2.11 of MSA.

(b)

Three special types of random variables. Chapter 2.3 of BPT.

i.

Discrete random variables. MSA Chapter 3.1, 3.2, 3.4 to 3.8 of MSA.

ii.

Absolutely continuous random variables. MSA Chapter 4.1, 4.2, 4.4 to 4.7 of MSA.

iii.

Vector valued random variables. BPT Chapter 2.6, 2.7, and 8.7. MSA Chapter 5.1, 5.2, 5.3, 5.4, 5.9, 5.10.

(c)

Distribution functions. BPT Chapter 2.5.

(d)

Functions of random variables. BPT Chapter 2.4, 2.8, 2.9 and 8.6. MSA Chapter 6.1 to 6.4, 6.6, 7.2.

4.

Expectation and Moments

(a)

Introduction. BPT Chapter 3.1.

(b)

Examples. BPT Chapter 3.2, MSA Chapter 3.3, 4.3, 4.9, 5.5, 5.6

(c)

Properties of Expectation. BPT 3.3 and 3.6. MSA 5.8.

(d)

Correlation and Covariance. BPT Chapter 3.4, MSA 5.7.

(e)

The Markov inequality and its consequences. BPT 3.7, MSA 3.11, 4.10.

5.

Conditional Probability and Expectation

(a)

Introduction BPT Chapter 4.1, 4.2.

(b)

Conditional Densities BPT Chapter 4.3

(c)

Conditional Expectation BPT Chapter 4.4, MSA 5.11

6.

Transform Methods and the Central Limit Theorem

(a)

Introduction BPT Chapter 5.1

(b)

Examples BPT Chapter 5.2

(c)

Moment generating functions. MSA Chapter 6.5

(d)

Characteristic Functions. BPT Chapter 5.3

(e)

The Central Limit Theorem. BPT Chapter 5.4, MSA Chapter 7.1, 7.3, 7.5.

7.

Hypothesis Testing BPT Chapter 8.1 and 8.2, MSA Chapter 10.1, 10.2.

(a)

Generic Example. MSA Chapter 10.3.

(b)

Neyman-Pearson Lemma. BPT Chapter 8.2, MSA Chapter 10.10 and 10.11

(c)

Attained Significance Levels. MSA Chapter 10.6

(d)

Parametric Hypothesis Testing.

i.

Test for the Mean in a Normal Population. MSA Chapter 10.8.

ii.

Test for the Difference of Means in a Normal Populations. MSA Chapter 10.8.

iii.

Tests concerning Variances in Normal Populations. MSA Chapter 10.9.

iv.

Tests for Proportions. PSE Chapter 9.3 and 9.4.

(e)

Nonparametric Hypothesis Testing. MSA, Chapter 15.

i.

Two-Sample Shift Model. MSA Chapter 15.2

ii.

Sign Tests

a.

Test for Matched Pairs. MSA Chapter 15.3

b.

Wilcoxon Signed-Rank Test for Matched Pairs. MSA Chapter 15.4

iii.

Rank-Sum Tests

a.

Wilcoxon Rank-Sum Test. MSA Chapter 15.5

b.

Mann-Whitney U Test. MSA Chapter 15.6

iv.

Tests for Randomness

a.

Total Number of Runs

b.

Runs Above and Below the Median

v.

Kolmogorov-Smirnov Tests for Goodness of Fit.

8.

Estimation of Parameters. BPT Chapter 8.3, MSA Chapters 8 and 9.

(a)

Interval Estimates. MSA Chapter 8.5

i.

Interval Estimates for Means in Normal Populations. MSA Chapter 8.8.

ii.

Interval Estimates for Variances in Normal Populations. MSA Chapter 8.9

iii.

Interval Estimates from Large Samples. MSA Chapter 8.6.

(b)

Point Estimates. BPT Chapter 8.3 and MSA Chapters 8 and 9.

i.

Methods of Deriving Point Estimates

a.

Maximum Likelihood Estimates. MSA Chapter 9.7

b.

Bayes Estimates. BPT Chapter 8.3.

c.

Minimax Estimates. BPT Chapter 8.3.

ii.

How Good is a Particular Estimator?

a.

Bias and Mean Square Error. MSA Chapter 8.2.

b.

Relative Efficiency. MSA Chapter 9.2.

c.

Consistency. MSA Chapter 9.3.

d.

Sufficiency. BPT Chapter 8.4 and 8.5, MSA Chapter 9.4.

e.

Rao-Blackwell Theorem. BPT Chapter 8.3, MSA Chapter 9.5.

9.

Linear Models, Curve Fitting and Estimation by Least Squares. MSA Chapter 11.

10.

The Analysis of Variance. MSA Chapter 13.