Math 170E: General Course Outline
Catalog Description
170E. Introduction to Probability and Statistics: Part 1 Probability Lecture, four hours. Requisites: courses 31A and 31B. The Math 170E and 170S two quarter probability and statistics sequence is aimed to equip MathEcon and Financial Actuarial majors with essential skills in these areas. Math 170E is an introduction to probability theory. Topics include discrete (binomial, Poisson, etc.) and continuous (Exponential, Gamma, Chisquare, normal) distributions, bivariate distributions, distributions of functions of random variables (including moment generating functions and Central Limit Theorem). Letter grading.
Textbook
Hogg, Tanis, Zimmerman Probability and Statistical Inference
Outline Updated 10/17
Schedule of Lectures
Lecture  Section  Topics 

1 
1.1 
Basic Properties of Probability 
2 
1.2 
Methods of Counting 
3 
1.3 
Conditional Probability 
4 
1.4 
Independence 
5 
1.5 
Bayes' Theorem 
6 
2.1 
Discrete Random Variables 
7 
2.2 
Expectation 
8 
2.3 
Examples of Expectation 
9 
2.4 
Binomial Distribution 
10 
2.5 
Negative Binomial Distribution 
11 
2.6 
Poisson Distribution 
12 
3.1 
Continuous Random Variables 
13 
3.2 
Examples: exponential, Gamma, Chisquare 
14 
Midterm on Chapters 1 and 2 

15 
3.3 
Normal Distribution 
16 
3.4 
Add'l models: failure rate, mortality, insurance 
17 
4.1 
Discrete bivariate distributions 
18 
4.2 
Correlation 
19 
4.3 
Conditional Distributions 
20 
4.4 
Continuous Bivariate Distributions 
21 
4.5 
Bivariate Normal Distribution 
22 
5.1 
Functions of a random variable 
23 
5.2 
Transformations of 2 random variables 
24 
5.3 
Several Random variables 
25 
5.4 
Moment generating functions 
26 
5.5 
Random functions associated to normal distributions 
27 
5.6 
Central Limit Theorem 
28 
5.7 
Approximations for Discrete distributions 
29 
5.8 
Chebyshev's inequality and convergence in probability 