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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 Math-Econ 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, Chi-square, 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, Chi-square

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