CS/SE 3341 Probability and Statistics in Computer Science

 Instructor: Michael Baron Teaching Assistant: Marzana Chowdhury Office: FO2.602-E Office: FO 1.210 Phone: 972-UTD-6874 Office hours: Monday 1-3 pm; Tuesday 2-5 pm

#### MuchLearning - homework assignments. Follow MuchLearning instructions.

Tables of Distributions

## Homework

Homework is assigned on MuchLearning.

## Quizzes and Exams

Quiz 1, solutions
Quiz 2, solutions
Quiz 3, solutions
Quiz 4, solutions
Midterm Exam, solutions
Quiz 5, solutions
Quiz 6, solutions
Quiz 7, solutions
Quiz 8, solutions
Quiz 9, solutions
Quiz 10, solutions

## FINAL EXAM SOLUTIONS

#### The Final Exam is on May 8, 5:00 - 7:00 pm. Here is a PRACTICE FINAL Ready for more practice? Here are additional exercises. The final exam covers topics: - Stochastic processes; counting processes - Binomial, Poisson processes - Markov chains - transition probabilities, steady-state distribution - Queuing processes - Bernoulli, M/M/1 - Statistics: parameter estimation, confidence intervals, hypothesis testing Notice that the 2nd part of the course is heavily based on the 1st part. So, practically, the exam is cumulative. Here is Prof. Baron's Cheat Sheet for the Final Exam which will be attached to your exams along with the tables of distributions. No other material is allowed on the exam.

Learn how to manage exam stress.

## Some Lecture Notes

(You may need Acrobat Reader to see and print these notes)

Notes 1 "Introduction. Probability rules."
Notes 2 "Equally likely outcomes. Conditional probability"
Notes 3 "Random variables and distributions"
Notes 4 "Discrete distributions"
Tables of Distributions
Notes 5 "Continuous distributions"
Notes 6 "Important continuous distributions" (updated on Feb 28)
Notes 7 "Stochastic processes. Bernoulli, Binomial, Poisson processes."
Notes 8 "Markov chains"
Notes 9 "Single-server queuing systems"
Notes 10 "Statistical inference"

Notes on Probability Rules
Notes on marginal and joint distributions
Notes on expected value and variance
Notes on discrete distributions
Notes on Binomial, Geometric, and Poisson
Examples on Binomial and Poisson distributions
Notes on Continuous Distributions
Examples on Normal distribution and Central Limit Theorem
Examples on Normal approximations and Binomial process
Example of a Markov chain
Bernoulli single-server queuing system
Markov chains and queuing systems examples
M/M/1 queuing system
Statistics: method of moments
Method of moments and Maximum likelihood
Estimation examples and Confidence Intervals
Hypothesis testing and confidence intervals
Final Review

## Matlab corner

• MATLAB programs used in our classroom demonstrations:
Markov chain for sunny and cloudy days
Markov chain for the game of ladder
Poisson process of arrivals
Bernoulli and Binomial processes
Brownian motion
Central Limit Theorem
• A Matlab tutorial

#### Recommended texts

• Probability and Statistics with Reliability, Queuing, and Computer Science Applications,
by K. Trivedi, John Wiley and Sons, New York, second edition (2002), ISBN 0471333417
• Probability and Statistics for Computer Scientists,
by M. Baron, Chapman & Hall/CRC Press (2007), ISBN 1584886412
• Concepts in Probability and Stochastic Modeling,
by J. J. Higgins and S. Keller-McNulty, Wadsworth Publishing House (1995), ISBN 0-534-23136-5
• Probability and Statistics for Engineering and the Sciences, seventh edition (2008) or eighth edition (2011),
by J. L. Devore, Duxbury, ISBN 0495557447 or 0538733527
These texts overlap, so you don't need to buy all of them. See the course syllabus for their comparison and coverage.