## 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. **

## Grading

Homework...25%

Exam 1.........25%

Exam 2.........25%

Final.............25%

## Course Outline

- Introduction
- Axioms of probability (chap 2)
- Counting techniques (chap 1) and applications to discrete
probability (chap 2)
- Conditional probability and independence (chap 3)
- Random variables and expectation (chap 4,5,7)
- Discrete random variables
- Continuous random variables

- Jointly distributed random variables (chap 6)
- Limit theorems (chap 8)