ENEE 324H Engineering Probability

ENEE 324H Engineering Probability

Spring 2018

Last Update - Sunday, April 29, 2018

Course Information

Special Announcements - most recent at the top

(12) Homework Set 11 has been posted. It is due in class on Tuesday, May 8.

Also do reading assignments from Ross and from Astrom (sent to you by email on April 26) and recalled here:

Karl Johan Astrom - Introduction to Stochastic Control Theory (ch2), and Sheldon Ross - Applied Probability Models with Optimization Applications (ch 2)

Reading assignment (1): First read Ross to understand general definitions concerning stochastic Processes (independent increments, stationary increments, etc), followed by two equivalent definitions of the Poisson process (pages 10 - 14 covered April 26, and pages 15-19 to covered during week of April 30).

Note that Ross uses upper case letters to denote random variables and the time index t for a stochastic process is a subscript and not an argument in parentheses. This is also my preferred notation.

Reading assignment (2): Read Astrom pages 13 - 20

Note that Astrom uses lower case letters even when indicating random variables and the time index is an argument in parentheses and not a subscript. This evokes a "signal processing style".

(11) Homework Set 10 is posted (and emailed to class).

(10) Homework Set 9 posted (and emailed to class).

(9) Homework Set 8 posted (and emailed to class). It is important to be up to date with assigned readings - now in Chapter 4.

(8) Before Spring Break we discussed Inequalities in class on Thursday March 15. Study material pertaining to this topic from PSK Lecture Notes, Lecture 6, and from Textbook Chapter 3 (Cauchy- Schwarz Inequality) before class on Tuesday March 27. We will also discuss material from PSK Lecture Notes and Chapter 4 pertaining to continuous reandom variables.

MidTerm II is scheduled for Thursday, April 5. Homework Set 7 will be assigned Tuesday March 27 and will be due back in class on Tuesday April 3.

Homework Set 7 posted.

(7) Homework Set 6 posted.

(6) Homework Set 5 posted. Extra class (optional) on integration - Tu 5:15 - 7:15 pm, A. V. Williams Building Room 2224. Material needed for discussion in depth of mutlivariate (or vector) continuous random variables.

(5) Homework Set 4 posted - due back Thursday February 22 in class. REMINDER - Mid Term Exam I in class, closed book, no calculators. Intermediate steps in calculations must be displayed in Homework Solutions and in the Exam - to avoid losing points.

(4) Homework Set 3 posted - due back Thursday February 15 in class.

(3) Homework Set 2 posted - due back Thursday February 8 in class. Also, in my Lecture Notes, Lecture 3, on Conditioning, make explicit determination of the sample space, in Example on Optimal Choice beginning on Page 2, and Hiking example on pages 7-9. The links below (interesting resources on the web) to the Wiki page on Monty Hall problem and the Stanford Encyclopedia article on Bayes' Theorem are strongly recommended.

(2) Homework Set 1 posted - due back Thursday February 1 in class.

(1) Read pages 1-8 of Chapter 1 of Grimmett and Stirzaker (textbook). Discussion on Wednesday January 24 will include this material.

(0) Textbook: Geoffrey Grimmett and David Stirzaker - Probability and Random Processes, Third Edition, Oxford University Press, 2001, (reprinted in 2004 with corrections) ISBN 0 19 857222 0 (paperback)

Lecture Notes by P. S. Krishnaprasad

- as supporting material for instruction and NOT as a substitute for the textbook

Lecture 1-6 and 10

Weekly Homework Assignments

Group effort in working out homework problems is acceptable. However everyone should submit individual homework solutions. Precise credit for any sources used (colleagues, teachers, journal articles, books, web resources etc.) should be given.

Running list of exercises.

Some interesting resources on the web

Wiki on Monty Hall Problem

Wiki on Bayesian Probability

Stanford Encyclopedia of Philosophy on Bayes' Theorem

Cornell site on Bayesian Inference for the Physical Sciences - somewhat dated