Math 481, Fall 2009: Syllabus

This syllabus will be updated as the semester progresses.

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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 Text Homework 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 CraMer-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