## Math/Stat 451 (Probability) . . . . Fall 2012

Instructor: Steve Krone . . . . Office hours: after class and by appt.
Office: 421 Brink Hall

Class Time:8:30 - 9:20 MWF
Place: REN 125

Text: S. Ross, A First Course in Probability, 8th ed.

Prerequisite: Calculus and a strong desire to learn.

This course deals with the mathematical description of random phenomena. It serves as the prerequisite for Math/Stat 452 (Mathematical Statistics) and Math/Stat 453 (Stochastic Models). While calculus is the only prerequisite, you should keep in mind that this is a 400 level mathematics course, so a certain amount of maturity (mathematical and otherwise) will be assumed.

Homework Assignments:
HW 2 (due W, Sept 12): Chap 2 Problems (pp: 52-53): 23, 29, 35 (a-c), 36. Show your work! For this homework, you should write down what the sample space is for each of the problems. In a multi-part problem, it might be the same sample space for each part.

HW 3 (due, W, Sept 19--not a full week): Chap 3 Problems (pp. 102-106): 29, 33, 53. As always, show your work, including using clear notation!
HW 3 Solutions

HW 4 (due Mon, Oct 8): Ch 4 problems (pp 172-176): 18, 25, 28, 40. You must show your work to get credit.

HW 5 (due Wed, Oct 24): Ch 5 problems (pp. 224-227) 1, 6bc, 15ab, 37a

HW 6 (due Wed, Oct 31): Ch 5 problem 32, Ch 7 problem 33, page 375, and the following problem: (a) If a r.v. has mgf M(t)=.4 exp(2t) + .6 exp(-3t), compute E(X). (b) If a r.v. X has pmf p(-1)=.2, p(0)=.3, p(1)=.5, compute its mgf M(t).

HW 7 (due Fri, Nov 16): Ch 6 problems (pp 287-288) 6.9 bce, 6.21 a.
Additional problem: Let X,Y have joint density f(x,y)=4/3(y+xy), for x in [0,1] and y in [0,1]. Find Cov(X,Y).

Problems to have you solve in class starting Mon: 6.40, 6.41a, 7.51, 7.64a, 7.65 (expected value part), 8.6, 8.7.

EXAM 1: Mon, Sept 24

EXAM 2: Mon, Nov 5

FINAL EXAM: Tue, Dec 11, 7:30-9:30 a.m.

Homework...25%
Exam 1.........25%
Exam 2.........25%
Final.............25%

## Course Outline

1. Introduction
2. Axioms of probability (chap 2)
3. Counting techniques (chap 1) and applications to discrete probability (chap 2)
4. Conditional probability and independence (chap 3)
5. Random variables and expectation (chap 4,5,7)
• Discrete random variables
• Continuous random variables
6. Jointly distributed random variables (chap 6)
7. Limit theorems (chap 8)