# 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 Text Homework 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