SECTION 02 of MATH 477, SPRING 2004

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01:640:477:02 Mathematical Theory of Probability — Spring 2004

Homework 1, 2, and 3 answers are posted below.
The probability distribution handout for hourly 2 is available in advance here. In addition, you will get a copy of the standard normal cumulative distribution function table. If there is something that you would like to see added to the handouts, let me know and I will consider it.
You can download the computations for probabilities for the game of craps here
3/3/04 -- There has been a significant revision of the answers to hourly 1 originally posted here. Please download and print out the revised version here (or from the link at the bottom of this syllabus)

Class Meetings: MTH3(11:30—12:50), ARC 205, Busch Campus
Lecturer: Barbara L. Osofsky, email: osofsky@math.rutgers.edu, telephone 732-445-3485.
Office Hours: Thursday 2nd period in Hill 710, or by appointment
Text: Sheldon Ross, A FIRST COURSE IN PROBABILITY, 6th edition, ISBN # 0-13-033851-6, Prentice-Hall.
Prerequisites: CALC III -- third-semester, multiple-variable calculus, which is Math 251 at Rutgers-NB -- is an essential prerequisite which we will not waive. A working knowledge of multiple integrals and partial derivatives is essential for the course.
Exams and Homework: There will be two midterm exams and a final exam, textbook homework, and possibly short unannounced quizzes, given in class and based on the assigned homework problems. If homework is late, it will lose 20% of the total value assigned to it for each day it is late. That is, if the homework is worth 10 and you hand it in 3 days late, then the grade you will get on it is the larger of 0 and (your earned score minus 6). There will be no make-ups for quizzes.
Grades: Your course grade will be determined by your total grade as follows:

Disclaimer: The information here is tentative and subject to change or confirmation by announcement in class.

Hand in exercises marked here with * .

Write out your answers neatly in complete English sentences. and explain your reasoning.

P: Problems TE: Theoretical Exercises

due 1/29	Chapter 1, P: 1,2,7,9,12,15,18,20,24,26,27,28* Chapter 1, TE: 2,8,13,14ab* (hand in both parts)
due 2/5	Chapter 1, P: 31 Chapter 2, P: 5,8,12,15d,16,18,20,25,28,33,36,37,39,41,46,50,52,55 Chapter 2, TE: 6, 9*
due 2/16	Chapter 2, P: 46 Chapter 3,P: 1,7,11,19,20,21,22,31,33,34,37,41,51, 58,62*,69,70,74,79A Chapter 3 TE: 5,7a
due 3/1	Chapter 4, P: 2, 4, 17, 18, 19, 20, 26, 28, 30, 33, 35, 40, 43 Chapter 4, TE: 5*, 6, 10 Chapter 4, STP: 1, 3, 10
due 3/8	Chapter 4, P: 21, 37, 38, 51, 53, 55, 58, 63, 65, 68, 74 Chapter 4, TE: 17b, 25, 26* (probabilistic interpretation)
due 3/25	Chapter 5, P: 1, 2, 4, 7, 11, 14, 15, 20, 22, 23, 27, 31, 32*, 37, 39
due 4/5	Chapter 5, P: 25, 29, 33, 40* Chapter 5, TE: 14, 21, 26, 30 Chapter 6, P: 9, 14, 18, 21, 22, 26, 27, 33
due 4/19	Chapter 6 P: 45, 49* Chapter 6 TE: 8, 10, 14 Chapter 7 P: 3, 9, 12, 14, 18, 21, 25, 30, 31
due 5/3	Chapter 7 P: 26, 34, 36, 40, 45, 48, 50 Chapter 7 TE: 13 Chapter 8 P: 1, 2, 3, 4, 5, 6, 7, 13, 14* Chapter 8 TE: 2, 6b, 14

Please note: This syllabus, and the midterm exam dates, are approximate; our mileage will vary. See the disclaimer for Textbook Homework.

A PDF version of the syllabus may be available for print-out.

#	Date	Reading	Topics
1	1/22	1.1--1.5	Counting
2	1/26	1.6, 2.1--2.3	More Counting; Axioms of Probability
3	1/29	2.4--2.5	Inclusion/Exclusion; Equally Likely Outcomes
4	2/2	2.5	Examples; Stirling's Formula
5	2/5	3.1--3.3	Conditional Probability; Bayes' Formula
6	2/9	3.4	Independent Events
7	2/12	3.5	Repeated Independent Trials
8	2/16	4.1--4.3, 4.9	Random Variables, Distribution Functions and C.D.F.'s
9	2/19	EXAM 1 --- Sections 1.1--3.5
10	2/23	4.4--4.6	Expectation and Variance of Discrete RV
11	2/26	4.7--4.8	Special Discrete RV's---Bern., Bin., Geom. Distributions
12	3/1	4.8	More Special RV's---Poisson, Neg. Bin., Hypergeom. d.f.'s
13	3/4	5.1, 5.2	Continuous RV's; Expectation and Variance
14	3/8	5.3--5.5	Special Cts RV's---Uniform, Expon., Normal d.f.'s
15	3/11	5.4	Normal Approximation to Binomial RV's
			SPRING BREAK 3/13—3/21
16	3/22	5.6, 5.7	Gamma RV's; Functions of a RV
17	3/25	6.1	Several RV's; Joint Distributions
18	3/29	6.2	Independent RV's
19	4/1	6.3	Sums of Independent RV's
20	4/5	7.1, 7.2	Linearity of Expectation
21	4/8	EXAM 2 --- Sections 4.1--6.3
22	4/12	7.3	Covariance and Correlation
23	4/15	6.4, 6.5	Conditional Distributions
24	4/19	7.4	Conditional Expectation
25	4/22	7.6	Moment Generating Functions
26	4/26	8.1, 8.2	Markov and Chebyshev Inequalities; Weak Law of Large Numbers
27	4/29	8.3	Central Limit Theorem
28	5/3	Catch up and review
FINAL EXAM (entire course): May 7, 8:00-11:00 AM; probably ARC 205