Math 481, Spring 2008: Syllabus

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The chapter and section numbers listed under "text" refer to John Freund's Mathematical Statistics with Applicationtion by Miller and Miller.

Link for a normal probability calculator.

Date Topics TextHomework
1 1/22 Probability review: Random variables; expectation;
means, variances, covariances; sums of r.v.'s;
Chapter 3, 3.2, 3.3, 3.4 especially
Chapter 4, 4.2, 4.3, 4.5, 4.7
Facts on distributions from chapters 5 and 6
Due 1/29
3.13, 3.22, 3.74, 3.75, 3.82
4.7, 4.19, 4.23, 4.33, 4.37, 4.38b), 4.48, 4.49
7.16, 7.17, 7.30
Solutions to Problem Set 1
2 1/24 Independent random variables and their joint densities;
Application of moment generating functions
to sums of independent r.v.'s;
Finding the density of u(X) from the density of X;
Chapter 7, 7.2, 7.3, 7.5  
3 1/29 Finding the density of Z=u(X,Y) Chapter 7, 7.4  
4 1/31 Sample mean, sample variance, central limit theorem
Confidence intervals, confidence interval for the mean
Chapter 8, 8.1, 8.2,
Due 2/5, Hand in bold-faced problems:
7.20, 7.30, 7.31, 7.34, 7.36
8.1, 8.2, 8.4, 8.5, 8.61, 8.64, 8.65, 8.67, 8.70, 8.71
Solutions to Problem Set 2
5 2/5 Sampling from finite populations;
Confidence intervals when variance is known; The chi square distribution
Chapter 8, 8.3, 8.4
Chapter 11, 11.1, 11.2
Due 2/12
8.13, 8.22/8.23/8.24(this is basically one problem)
8.25, 8.26,8.28, 8.31, 8.33, 8.75, 8.76, 8.79 11.1, 11.4, 11.5, 11.20, 11.21, 11.22, 11.30. 11.31, 11.34
Solutions to Problem Set 3
(Note: Mistake in 11.34 corrected, 2/25.)
6 2/7 Sampling from a finite population
The chi-square and t-distributions
Confidence intervals for the mean when variance is unknown
Chapter 8: 8.3, 8.4, 8.5
Chapter 11: 11.2, 11.3
 
7 2/12 Confidence intervals for the variance
and for the difference of means;
F-distributions and confidence intervals for ratio of variances
Chapter 8, 8.6
Chapter 11, 11.6, 11.7
Homework due 2/19
8.31, 8.39, 8.40, 8.41, 8.42, 8.43, 8.44/8.86, 8.45, 8.46, 8.50, 8.53, 8.54/8.88, 8.81
11.55, 11.57
Solutions, Problem Set 4
8 2/14 Order statistics; sampling from a finite population Chapter 8: 8.3, 8.7  
9 2/19 Confidence intervals for proportions; Point Estimates, unbiased estimates; efficiency Chapter 11: 11.4 and 11.5
Chapter 10: 10.1-10.3
Homework due THURSDAY, Feb 21: 11.12, 11.16. 11.38, 11.39, 11.40, 11.45, 11.49
Solutions to Problem Set 5
10 2/21 Efficiency, consistencey and sufficiency Chapter 10: 10.3, 10.4, 10.5  
11 2/26 FIRST MIDTERM Solutions to Midterm I Extra problems on material of Midterm I
12 2/28 Sufficiency Chapter 10: 10.5 Homework due March 4
10.1, 10.3, 10.6, 10.8, 10.13, 10.14, 10.15, 10.17
10.21, 10.22, 10.23, 10.24, 10.26, 10.43
Solutions to Problem Set 6
13 3/4 Method of moments;
Maximum likelihood
Chapter 10: 10.4, 10.7, 10.8 Problems due March 11:
10.33, 10.36, 10.37, 10.42, 10.43, 10.45,
10.48, 10.49 10.51, 10.53, 10.56,
10.59,, 10.62, 10.66, 10.71, 10.72
Solutions to Problem Set 7
14 3/6 Chapter 10: 10.8 Maximum likelihood  
15 3/11 Hypothesis testing: introduction Chapter 12:12.1, 12.2 Problems due 3/25:
12.1, 12.3, 12.4, 12.5, 12.6, 12.7, 12.10, 12.11
12.12, 12.13, 12.15, 12.32
Solutions to Problem Set 8
16 3/13 The Neyman-Pearson lemma Chapter 12: 12.4  
17 3/25 Tests with composite hypotheses;
Power functions; likelihood ratio tests
Section 12.5, 12.6 Problems due, April 1
12.18, 12.20, 12.21, 12.22, 12.24,12.25, 12.41
Solutions to Problem Set 9
18 3/27 Power functions and likelihood ratio tests Sections 12.5 and 12.6
Class note about interpreting power functions
 
19 4/1 Testing hypotheses on means, variances, proportions Sections 13.2, 13.2, 13.4, 13.5  
20 4/3 SECOND MIDTERM Information on second midterm  
21 4/8 Testing hypotheses on k-proportions, tables Sections 13.6, 13.7  
22 4/10 Testing hypotheses on k-proportions, tables
Goodness of fit
Section 13.8 Problems due 4/15
13.20, 13.21, 13.25, 13.26, 13.38, 13.40