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36-217 Probability Theory And Random Processes Homework

36-217: Probability Theory and Random ProcessesCourse DescriptionThe theory of probability and random processes provides the mathematical tools needed to model uncertainty in virtually all scientiFc areas. Nowadays, probabilistic models are key for the development and analysis of scientiFc theories and of many algorithms, with countless applications, including the analysis of network dynamics of circuit failure rates, the development of algorithms for computer vision, machine learning, image processing, cryptography, system performance assessment, business inventory, marketing, Fnance, medicine, etc.This is a Frst course in probability theory that is designed to prepare you to develop and analyze basic probabilistic models for describing and studying uncertain or random phenomena and to make better predictions and decisions. By the end of this course, you will1.Possess an adequate background and understanding of basic concepts in probability theory;2.Be able to apply probability terminology and formalism correctly to represent elementary random experiments and quantify uncertainty;3.Be proFcient in the calculus-based mathematical skills needed to solve problems in basic probability.Course Objectives1.Basic Probability.•Describe the sample space of an experiment using set notation.•±ind the probabilities of complements, unions, and intersections of events.•Use counting tools to enumerate the number of equally likely outcomes of simple experiments.•Use the law of total probability and Bayes’ Rule to calculate probabilities.•DeFne and identify independence of events.•Calculate conditional probabilities of events.2.Random Variables•Describe the random variable associated with a question of interest.•Describe and identify discrete and continuous random variables.


Lecture Times : Every weekday 12p-1:20p
Classroom: Porter Hall A18c

Instructor: Sangwon Hyun
Office Hours: Every weekday 1:20p-2p, and by appointment (Porter Hall A18C)

TA: Zongge (John) Liu (zonggel@andrew.cmu.edu)
Office Hours: Monday and Wednedsay, 4:00p-5:00p (Wean Hall 8419)

Announcements & Grades
Check blackboard for all announcements and grades.

Syllabus
The syllabus.pdf contains the overview, basic information and requirements of the course.

Lecture Notes & Homework
Lecture notes are updated frequently, so check back often. Homeworks are inserted in the correct chronological place (of their due date). master.pdf

Solutions
Homework and practice problem solutions will be posted shortly after they are due. No late homeworks will be accepted. master-hwsol.pdf

Midterm Practice
Here is a practice midterm (with and without solutions). Other good sources of practice is homeworks and in-class exercises, and book problems relevant to the assigned readings. midterm-practice.pdf midterm-practice-sol.pdf

Midterm Solutions
Are here: midterm-sol.pdf

Final Practice
Here is a practice final exam. practice-final.pdf

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