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Math 231 Syllabus Fall, 2003 Textbook: Probability and Statistics for Engineers and Scientists, by Walpole, Myers, Myers, and Ye. Seventh Edition, Prentice Hall Section Topic Selected Problems Chapter 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Populations and samples The role of probability Sampling: collection of data Measures of location: sample mean Measures of variability Discrete & continuous data Statistical modeling Graphical methods. 2, 4 p.20 7 p.20 10 p.20 Chapter 2. 2.1 2.2 2.3 Sample spaces Events Counting sample points 4, 6, 8 p.29 10, 14, 19, 20 p.30-31 4, 6, 11, 12, 14, 17, 18, 20, 23, 26, 27, 29 p.38-39 2.4 2.5 2.6 2.7 Probability of an event Additive rules Conditional probability Multiplicative rules 2.8 Bayes' rule Review exercises 2, 3, 6, 8, 13, 15, 17, 18, 22, 23 p.54-56 1, 3, 6, 7 p.60-61 1, 2, 5, 8, 10, 13 p.61-62 Concept of a random variable Discrete Probability distributions Continuous probability distributions Joint probability distributions Review exercises 2, 4, 11, 12, 15, 24 p.72-74 6, 7, 14, 21 p.73 3, 4, 5, 9, 13, 18, p.84-85 2, 3, 4, 7 p.86 4, 5, 8, 12, 13, 16, p.46-47 Chapter 3. 3.1 3.2 3.3 3.4 Chapter 4. 4.1 Expected value of random variable 4.2 4.3 4.4 Variance and covariance Linear combinations of r.v.'s Chebyshev's theorem 2, 4, 8, 9, 12, 14, 19, 20, 21, 26, p. 94-95 2, 3, 6, 11, 13, 16 p.102-103 3, 6, 11, 13, 14, p.112-113 17, 18 p.113 Math 231 Syllabus (continued) Section Topic Selected Problems Chapter 5. 5.1 5.2 5.3 Introductions Discrete uniform distribution Binomial & multinomial distributions 5.4 5.5 5.6 Hypergeometric distribution Negative binomial & geometric dists. Poisson distribution Review exercises 2, 5, 9, 12, 14, 16, 18, 22 p.124-126 4, 7, 9, 14, 16, 19 p.131-132 1, 2, 5, 9,14,20, 23 p.139-140 14, 16 p.140-141 Chapter 6. 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Continuous uniform distribution Normal distribution Areas under the normal curve Applications of normal distribution Normal approximation to binomial Exponential distribution Applications of exponential distribution (Omit gamma distribution) 6.8 Chi-Squared distribution (Omit 6.9-10) Review exercises 2, 4, 6 p.156-157 7, 9, 10, 12, 18, 22 p.157-8 1, 2, 4, 8, 12, 13, 14 p.164-5 7, 8, 15 p. 174-175 2, 4, 5, 7, 10 p. 175-176 Chapter 7. Omit this chapter BUT read pages 190 and 191. Chapter 8. 8.1 8.2 8.4 8.5 8.6 8.7 Random sampling Some important statistics (Omit 8.3, read pages 201-207) Sampling distributions Sampling distribution of mean Sampling distribution of variance t distribution (Omit 8.8) 2 p.200 4, 9, 14 p.200-201 1, 2, 4, 5, 7, 9, 12, 14 p.215-6 2, 4, 5, p.227 8, 11, 13, 14 p.228 Math 231 Syllabus (continued) Section Topic Selected Problems Chapter 9. 9.2 9.3 9.4 9.5 Statistical inference Methods of estimation Estimating the mean Standard error (Omit 9.6-8) 9.9 Paired observations 9.10 Estimating a proportion (Omit 9.11-15) (read 9.12 on estimation of variance) 2, 4, 5, p.245 6, 8, 9, 13, p.245-6 11, 12 p.256-257 1, 2, 4, 6, 9 p. 262-3 Chapter 10. 10.1 10.2 Statistical hypotheses Testing a statistical hypothesis 10.3 10.4 10.5 10.6 10.7 One- and two- tailed tests P-value Tests concerning a mean Relationship to confidence interval Tests on a mean (variance unknown) (Omit 10.8-18) (read Table 10.2 on page 313) Chapters 11-17 (Omit entirely) 2, 3, 4, 6, 12, 14, p.298-299 1, 2, 4, p.319 11, 25, p.319-321