Download Math 231 Syllabus Fall, 2003

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