Download Math 231 SYLLABUS Fall 2001

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