# MATH 151 - Introduction to Probability Theory

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### Scope and Aim:

A first course in probability theory, similar in content to STAT116, but with more emphasis on mathematical foundations and analytical manipulations. Material covered: Probability spaces as models for uncertainty, and introduction to the corresponding mathematical analysis. Combinatorial analysis for discrete spaces (binomial, Poisson, geometric). Conditional probabilities and stochastic independence. Random variables and expectation. Law of large numbers, Normal and Poisson approximations. Continuous spaces (normal, exponential, uniform) and densities.

### Prerequisite:

Maturity in analysis, reflected by passing MATH52 at A- or higher grade, or the consent of instructor.

### Meetings:

MWF 2:15-3:05, Herrin Hall (Biology), T195.

### Text

Ross: A first course in probability, 9th edition, 2012 (you may use the 8th or 7th editions, but be responsible for finding which problem in your copy matches the assigned homeworks).

### Alternative Text

Pitman: Probability, Springer Verlag, 1993;

For applets and notes prepared by Susan Holmes for teaching a similar class on the web click

### Final exam: (solution) : Monday, March 16, 12:15-3:15PM, Herrin Hall, T195.

Material: 1.1-1.5,2.1-2.5,3.1-3.5,4.1-4.10,5.1-5.7,6.1-6.5,6.7, 7.2[without 7.2.1-7.2.2],7.4-7.5,7.7,7.8.1,8.2-8.3 of text.

The exam has 6 questions, each somewhat harder and longer than an average homework problem.

### You can bring to the exam your HWs, their posted solution, a text book, your class notes and calculator.

Practice exam: Try 3h timed solution of following 8 problems from "Self-Test Problems" in text-book: 2.3,3.14(or 3.15),4.17(or 4.28),5.9(or 5.17),5.14,5.22(or 6.15), 6.9(or 6.12, or 7.25),7.4(or 7.27).

Alternatively, try 3h times solution of Final 2014, then compare with its solution.

30% Homework
70% Final

Letter grade based on relative standing of the combined numerical work.

### Homeworks:

Homework problems from text are due in class, Friday 2:15PM on a weekly basis (about 10 problems/week, starting January 16). Late homework will not be accepted (each correct homework problem earns credit, so submit even partial solutions!). See page 433 of text for final answer of most problems, but to get homework credit you must provide detailed derivations. Students may collaborate in solving the homework, but should independently write their own solutions.

Homework 1.40 denotes Problem 40 at the end of Chapter 1 of the text, while 2.T.3 is Theoretical Exercise 3 at the end of Chapter 2, and so on. Number of problems in each HW set will also be indicated in brackets below.

All homework solutions posted; All graded works returned in class (by FRI 3/13, lecture).

• HW1 due 1/16: 2.2,2.5,2.15,2.19,2.23,2.31,2.46,2.53,2.T.16[9] (solution).
• HW2 due 1/23: 3.14,3.23,3.28,3.41,3.44,3.60,3.67,3.74,3.90,3.T.7,3.T.30[11] (solution).
• HW3 due 1/30: 4.6,4.21,4.26,4.33,4.42,4.78,4.T.13,4.T.16,4.T.21,4.T.27[10] (solution).
• HW4 due 2/6: 4.62,4.65,4.67,4.69,4.72,4.76,4.T.25,4.T.28,4.T.32,4.T35[10] (solution).
• HW5 due 2/13: 5.4,5.5,5.8,5.10,5.16,5.22,5.26,5.31,5.34,5.36[10] (solution).
• HW6 due 2/20: 5.41,5.T.5,5.T.11,5.T.13,6.6,6.9,6.13,6.15[8] (solution).
• HW7 due 2/27: 6.16,6.18,6.20,6.22,6.24,6.25,6.28,6.31,6.T.8,6.T.11[10] (solution).
• HW8 due 3/6: 6.41,6.43,6.45,6.46,6.52,6.T.19,6.T.20,7.2,7.8,7.12,7.17[11] (solution).
• HW9 due 3/11: 7.25,7.26,7.42,7.44,7.48,7.53,7.69,7.72,7.75,7.T.10,7.T.11[11] (solution).

### Preliminary syllabus:

```    1/5      M(1.1-2.3)      W(2.4;2.5)          F(3.2;3.5)
1/12     M(3.3,3.4)      W(3.4;4.1;4.2)      F(4.3-4.6;4.9)
1/19     M(--)           W(4.7-4.8.2)        F(4.8.3-4.9)
1/26     M(4.10;5.1)     W(5.2;5.3;5.5)      F(5.2;5.3;5.5.1)
2/2      M(5.4;5.4.1)    W(5.7;6.1;6.2)      F(6.1;6.2)
2/9      M(6.3;5.6.1)    W(6.3;6.4)          F(6.4;6.5)
2/16     M(--)           W(6.7)              F(6.7;5.6.4)
2/23     M(7.2)          W(7.4)              F(7.5.1;7.5.2)
3/2      M(7.5.3;7.5.4)  W(7.7)              F(7.8.1;8.3)
3/9      M(8.3;8.2)      W(5.6.2-5.6.4)      F(Review)
```