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 Applications by Miller and Miller. Homework problems listed in bold face should be handed in.

Link for a normal probability calculator.

Link for a chi-square probability calculator. (Click on "Utilities," then on "Statistical Tables Calculator," then on "chi-square to P.")


Date Topics TextHomework
1 9/2 Probability review: Random variables; expectation;
means, variances, covariances; sums of r.v.'s;
moment generating functions 		Chapter 3, 3.2, 3.3, 3.4
Chapter 4, 4.2, 4.3, 4.5, 4.7
 Due 9/9
3.13, 3.22, 3.32, 3.33, 3.50, 3.51, 3.74(a), 3.75(a),
4.7, 4.19, 4.23, 4.33, 4.35, , 4.48, 4.49
Solutions to Problem Set 1
2 9/8 (Tuesday!) Multi-variate random variables
Expectation 		Chapters 3 and 4 Due 9/16
7.1, 7.5, 7.16, 7.17, 7.20(b), 7.29, 7.30, 7.31, 7.34, 7.36, 8.64
Solutions to Problem Set 2
3 9/9 Moment generating functions
Finding the density of Z=u(X,Y) or Z=u(X)		 Chapter 7, 7.2, 7.3, 7.4 See previous lecture
4 9/14 Sample mean, sample variance, central limit theorem
Confidence intervals, confidence interval for the mean		 Chapter 8, 8.1, 8.2
Chapter 11, 11.2,pp 355-357 		Due 9/23
8.1, 8.2, 8.3, 8.4, 8.5, 8.61, 8.67, 8.70, 8.71, 11.1, 11.2, 11.20, 11.21
Solutions to Problem Set 3
5 9/16 Sample mean, sample variance, central limit theorem
Confidence intervals, confidence interval for the mean		 Chapter 8, 8.1, 8.2
Chapter 11, 11.1, 11.2		  
6 9/21 Finite population sampling
Confidence intervals, confidence interval for the mean
Confidence intervals when variance is known; 		Chapter 8, 8.1, 8.2
Chapter 11, 11.2, 11.4, 11.5		 Due 9/30
11.3, 11.12, 11.22, 11.29, 11.38, 11.39, 11.40, 11.45, 11.49, 11.50
7 9/23 Confidence intervals;
Chi-square distribution, sample variance
Confidence intervals for variance 		Chapter 8: 8.3, 8.4
Chapter 11: 11.6		 Due 9/30
8.22/8.23/8.24 8.25, 8.26, 8.28, 8.75, 8.77
11.53, 11.54
Solutions to problems due 9/30
8 9/28 t-distributions and confidence intervals;
F-distributions and confidence intervals;		 Chapter 8, 8.5, 8.6
Chapter 11, 11.3, 11.6, 11.7		 Due 10/7:
8.30, 8.31, 8.33, 8.39, 8.40, 8.41, 8.42, 8.79, 8.81
11.6, 11.25, 11.30, 11.31, 11.32, 11.34, 11.57
Solutions, Problem Set 5
9 9/30 Order statistics; sampling from a finite population Chapter 8: 8.3, 8.7 Due 10/7: 8.13, 8.15, 8.43, 8.44/8.86, 8.45, 8.46, (Solutions are above)
Due 10/14: 8.50, 8.53, 8.54/8.88, 8.89
Solutions, Problem Set 6
10 10/5 Point Estimates, unbiased estimates; efficiency Chapter 10: 10.1-10.3 Due 10/14: 10.1, 10.3, 10.4, 10.5, 10.8, 10.13
11 10/7 Efficiency, consistency Chapter 10: 10.3, 10.4 Due 10/21: 10.12, 10.14, 10.15, 10.17
10.21, 10.22, 10.23, 10.24, 10.26
12 10/12 FIRST MIDTERM, in class Formula sheet for test
Review sheet for test
Chi-square and normal samples, lecture notes
Review prob. solutions, Part I,
Solutions, Part II 		 
13 10/14 Point Estimates, unbiased estimates; efficiency Chapter 10: 10.1-10.3 Due 10/21: 10.1, 10.3, 10.4, 10.5, 10.8, 10.13
14 10/19 Craner-Rao lower bound;
Sufficiency 		Chapter 10: 10.3, 10.4, 10.5 Due 10/21: 10.12, 10.14, 10.15, 10.17
10.21, 10.22, 10.23, 10.24, 10.26
Solutions, Problem Set 7
15 10/21 Method of moments;
Maximum likelihood 		Chapter 10: 10.4, 10.7, 10.8 Due 10/28: 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 8
16 10/26 Hypothesis testing: introduction Chapter 12:12.1, 12.2 Due 11/4: 12.1, 12.3, 12.4, 12.5, 12.6, 12.7,
Solutions to Problem Set 9
17 10/28 The Neyman-Pearson lemma Chapter 12: 12.4 Due 11/11: 12.10, 12.11
12.12, 12.13, 12.15, 12.32
18 11/2 Tests with composite hypotheses;
Power functions; likelihood ratio tests		 Section 12.5, 12.6 Due 11/11: 12.18, 12.20, 12.21, 12.22, 12.24,12.25, 12.41
Additional problems
Plot to go with additional problems Solutions to Problem Set 10
19 11/4 Power functions and likelihood ratio tests Sections 12.5 and 12.6  
20 11/9 Testing hypotheses on means, variances, proportions Sections 13.2, 13.2, 13.4, 13.5  
21 11/11 Testing hypotheses on means, variances, proportions Sections 13.2--13.5 Due 11/18: 13.19, 13.20, 13.21, 13.25, 13.26
Solutions, Problem Set 11
22 11/16 SECOND MIDTERM Information on second midterm  
23 11/18 Testing hypotheses on k-proportions, tables
 Section 13.6, 13.7 Due 11/23
13.2, 13.9, 13.38, 13.40 13.47
13.48, 13.54, 13.67, 13.73, 13.77, 13.78
24 11/23 Testing hypotheses on k-proportions, tables
 Section 13.6, 13.7 Due 11/23
13.2, 13.9, 13.38, 13.40 13.47
13.48, 13.54, 13.67, 13.73, 13.77, 13.78
Solutions to Problem Set 12
25 11/30 Regression, Least Squares, Normal Regression,
Bivariate normal		 Sections 14.1, 14.2, 14.3, 14.4, 6.7 Problems due 12/7
13.81, 13.83, 14.1, 14.3, 14.7, ,14.16, 14.52, 14.55
Solutions to Problem Set 13
26 12/2 Normal correlation analysis Section 14.5 Due 12/7: 6.45, 6.47, 14.31, 14.65, 14.66
Solutions to Problem Set 13
27 12/7 One way designs and analysis of variance Sections 15.1, 15.2  
28 12/9 Analysis of variance: One way layout Sections 15.2 Due 12/9: 15.17, 15.3, 15.19, 15.23
Solutions to Problem Set 14
29 12/14 FINAL EXAM EXAM REVIEW
Monday, Dec. 14, 1-3, Hill 124