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Course Outline

Grading Policies

Lectures

Homework Problems and Solutions

Student Projects

Resources

Exams

Piazza

Date

Concepts

Notes

Homework

In-class Activity

Mini Projects + Final Project

Jan 18

Probability Theory Basic

Lecture 1

Jan 23

Algebra of Events
Probability Axioms
Steps to problem solving
Combinatorial Problems

Lecture 2

Jan 25

HW 1

HW 1 solution

Jan 30

Conditional probability
Bayes formula
Total probability

Lecture 3

Feb 1

Independence and mutual exclusivity
Mini project 1 description

Lecture 4

HW 2

HW 2 Solution
(NOT Graded)

Mini Project 1 Posted

Feb 6

Reliability evaluation applications

1. Series systems
2. Parallel redundancy

Lecture 5

Group Activity 2

Solution

Feb 8

Reliability evaluation applications

1. Series systems
2. Parallel redundancy

Lecture 6

(pptx)

Feb 13

3. Series-parallel system evaluation
4. Non-series-parallel systems

Bernoulli Trials
Triple Modular Redundancy (TMR)

Lecture 6 (continued)

Lecture 7

Feb 15

More Reliability Application Examples

Lecture 8

HW 3

Solution

Group Activity 3

Solution

Feb 20

Introduction to random variables
Discrete and Continuous Random variables
Probability Mass Functions (PMF)

Cumulative distribution function (CDF)

Probability mass function

Intro to probability density function (PDF)

Discrete Random Variables

Continuous random variables

Lecture 9 and GA3 solution

Feb 22

• Important discrete random variables:
  • Bernoulli and Binomial Distributions
  • Poisson Distribution
  • Geometric & Modified Geometric Distr.
  • Derivation of Poisson using Binomial

Lecture 10

(pdf)

HW 4

(pdf)

Solution

Feb 27

• Examples on PDF, PMF and CDF
• Examples on Geometric RV

Lecture 11

Mar 1

1. Probability density function (PDF)
2. Important continuous random variables
3. Gaussian (Normal) Distribution

Lecture 11

HW5

Solution

Group Activity 4

Solution

Mini Project 2 posted

Mar 6

Exponential Distribution

• Gaussian (Normal) Distribution
• Exponential Distribution
• Memory-less property
• Relationship to Poisson distribution

Lecture 12

HW 6

(pdf)

(Solution)

Mar 8

• Hypo-exponentials
• Examples: TMR vs. TMR/simplex as hypo-exponentials

Lecture 13
 

Mar 13

Midterm Review

Lecture 14

HW6 due

Info on Binomial to Poisson conversion

http://courses.wcupa.edu/rbove/Berenson/10th%20ed%20CD-ROM%20topics/section5_6.pdf

Mar 15

Midterm Exam – In class

Midterm Exam

Mar 27

Midterm feedback

Erlang
Gamma
Hyper-exponential
Examples

Lecture 15

Midterm feedbacks

Midterm solution

Mar 29

Expectations: Introduction

Lecture 16

HW 7: Redo the midterm for Questions that had less than 60% of the total grade.

Deadline to request a midterm regrade request, 5pm Mar 29. Drop your midterm at 246 or 258 CSL.

Quiz 2

Quiz 2 Solution

Apr 3

Reliability evaluation applications:

• Mean time to failure
• Failure rates
• Hazard functions

Moments: Mean and variance
Mean/variance of important random variables
Functions of random variables

Lecture 17

Apr 5

Joint Distribution Functions
Independence of Random Variables
Covariance and Correlation

Lecture 18

In-class Group Activity 5

In-class Group Activity 5 solution

HW 8

HW 8 pdf

HW 8 solution

HW 7: Redo midterm (paper) due in class.

Apr 10

Joint probability distributions

Lecture 19

Apr 12

Joint Probability Distributions

Binary Hypothesis Testing

Lecture 20

HW 9

HW 9 (Solution)

Apr 17

Types of Errors

Receiver Operating Characteristics (ROC) Curve

Binary Hypothesis Testing (continued)

Maximum Likelihood and Maximum a Posteriori

Lecture 21

Apr 19

Binary Hypothesis Testing (cont.)

Lecture 22

HW 10

HW 10 (Solution)

Group Activity 6

Group Activity 6 (Solution)

HW9 due

Apr 24

Limit Theorems

Proof of Central Limit Theorem

Lecture 23 and 24

Apr 26

Limit Theorems (cont.)

Markov Inequality

Lecture 25

HW 10 due

May 1

Final Exam Review

Lecture 26

Problems on covariance and correlation

Problems on joint distributions

May 3

Final Exam Review

Lecture 26 (cont.)

Lecture 27

Final Project Presentation: 12pm - 4pm

Location: 1013 ECEB

Final Exam: 8:00am - 11:00 am

Location: 2015 and 2017 ECEB