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Math 231 SYLLABUS Fall 2001 Textbook : Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross Section Topic Homework Problems Chapter 1 1.1 1.2 1.3 1.4 Introduction Data and descriptive statistics Statistical inference and probability Populations and samples 1, 2, 5, 10 pages 7-8 Chapter 2 2.1 2.2 2.3 2.4 2.5 2.6 Introduction Describing data Sample mean, median, stand.dev. Chebyshev’s inequality Normal data Paired data and corr. coeff. 1, 3, 6abc p.40-43 6defg, 12, 14, 16, 19 p.43-49 29 p.57 24, 25 p.53 33, 36 p.57 Chapter 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Introduction Sample spaces and events Venn diagrams of events Axioms of probability Equally likely outcomes Conditional probability Bayes’ formula Independent events 1, 3, 6 p.82-83 9 p.83-84 14 p.84 15, 16, 18, 19, 21, 22 p.84-85 25, 26 p.85 27, 29, 31, 33, 34, 35 p.85-87 36, 39, 41, 45 p.87-88 Chapter 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Random variables Types of random variables Joint probability distributions Expectation (Omit Example 4.4c) Properties of expected values Variance Sums of random variables Omit The law of large numbers 1, 2, 4 p.127-128 6, 7, 36 p.128-133 9, 10, 12, 13, 17 p.129-130 21, 24, 25, 27, 28 p.130-131 31, 42 p.131-133 44, 45 p.133-134 51, 52 p. 135 55, 56 p.135-136 SYLLABUS(continued) Section Topic Homework Problems Chapter 5 5.1 5.2 5.3 5.4 The binomial distribution 1, 4, 5, 6, 8 p.184-185 The Poisson distribution 10, 13, 15 p.185 The hypergeometric distribution 18 p.186 The uniform distribution 22 p.186 (Omit Example 5.4d) 5.5 The normal distribution 23, 24, 27, 28, 34, 36 p.186-188 5.6 The exponential distribution 37, 38 p.188 (Omit Section 5.6.1) 5.7 Omit 5.8 Chi-square and t distributions 43, 46 p.189 (Omit Sections 5.8.1.1, 5.8.3) Omit all references to moment-generating functions in Chapter 5 and later. Chapter 6 6.1 6.2 6.3 6.4 6.5 6.6 Introduction The sample mean The central limit theorem The sample variance Sampling distributions Omit Chapter 7 7.1 Introduction 7.2 Maximum likelihood estimators 7.3.1 Confidence intervals for a mean (Omit Example 7.3g) 7.3.2 Interval for the normal variance 7.4 Omit 7.5 Confidence interval for a proportion (Omit Table 7.2) 7.6-7.8 Omit Chapter 8 8.1 8.2 8.3 8.4 Introduction Significance levels Tests concerning the normal mean Omit 1 p.210 3, 4, 5, 8, 12, 13, 24 p.210-214 18 p.212 1, 3, 5, 7 p.258-259 8, 11, 12, 13, 14, 17 p.260-262 36 p.264 48, 50, 55 p.267-268 9 p.311 1, 4 p.309-310 3, 5, 6, 10, 11, 14, 17, 21 p.310-313 SYLLABUS(continued) Section 8.5 8.6 8.7 Topic Tests concerning a normal variance (Omit Section 8.5.1) Tests concerning a proportion (Omit Section 8.6.1) Omit Chapters 9 –10 47 p.319 55, 57, 58, 59 p.321-322 Omit Chapter 11 11.1 Introduction 11.2 Goodness of fit tests (Omit Section 11.2.1) 11.3 Omit 11.4 Tests for independence 11.5-11.6 Omit Chapters 12-14 Homework Problems Omit 1, 2, 4, 5, 9, 10 p.470-473 16, 19 p.474-475