Tufts University
Department of Electrical and Computer Engineering
EE-193: Applied Probability and Statistics for Engineers
Fall 2007

Overview
Times and places
Staff
Prerequisites
Class requirements
Texts
Links
Preliminary schedule

Problem sets and solutions

Problem set 01 and solutions and Matlab code
Problem set 02 and solutions and mash.m and matlab driver
Problem set 03 and solutions
Problem set 04 and solutions and Matlab code
Problem set 05 and solutions
Problem set 06 and solutions
Problem set 07 and solutions
Problem set 08 and solutions
Problem set 09 and solutions
Problem set 10 and solutions

Overview

The goal of this class is the development of basic analytical tools for the modeling and analysis of random phenomena and the application of these tools to a range of problems arising in engineering, manufacturing, and operations research. The first portion of this class will cover introductory probability theory including sample spaces and probability, discrete and continuous random variables, conditional probability, expectations and conditional expectations, and derived distributions. From this foundation we shall explore basic random processes including the Bernoulli, Poisson, and introductory Markov processes. Correlation analysis will be discussed. The balance of the class will be concerned with statistical analysis methods including hypothesis testing, confidence intervals and nonparametric methods.

Times and places

Lectures

Tuesday/Thursday 10.30 AM -11.45 AM, 111-A Halligan Hall

Office hours

Tuesday/Thursday 1.30 PM - 2.30 PM, Prof. Miller's office
By appointment

Staff

Lecturer:

Prof Eric Miller
elmiller at ece dot tufts dot edu
216 Halligan (eventually)
Phone: 617.627.0835

Prerequisites

Calculus (Math 11, 12, and some of 13). Knowledge of differentiation and integration of single and multi-variable (mostly two variables) functions will be assumed throughout the class.
Matlab

Class requirements and preliminary grading

Problem sets: 20%
Midterm 1: 20%
Midterm 2: 20%
Final exam: 40%

Texts

Required text

Probability and Stochastic Processes, A Friendly Intriduction for Electrical and Computer Engineers, by Roy Yates and David Goodman, 2nd Edition, Wiley, 2005.

Other references

Probabilistic Methods of Signal and System Analysis, by George R. Cooper and the late Clare D. McGillem, Oxford, 1998
Introduction to Probability, by Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2002
Probabilistic Systems and Random Signals by A. H. Haddad, Prentice Hall, Upper, 2006
Probability and Random Processes for Electrical Engineering by Leon Garcia, Addison Wesley, 1994
First Course in Probability, by Sheldon Ross, Prentice Hall, 2005

VERY Preliminary Schedule

Date	Topic	Distributed/due
Sept. 4	Introduction and basic set theory
Sept. 6	Probability axioms, conditional probability, and independence
Sept. 11	Combintorics and discrete random variables
Sept. 13	Probability mass functions, discrete derived distributions, and expectations
Sept. 18	Expectations and continuous random variables
Sept. 20	Probability density functions and derived distributions
Sept. 25	Expected values, Gaussian random variables, and conditioning
Sept. 27	Joint probility models for pairs of random variables
Oct. 2	Derived distributions for pairs of random variables and conditioning
Oct. 4	Conditioning and independence
Oct. 9	NO CLASS: MONDAY SCHEDULE IN EFFECT
Oct. 11	Sums of random vaiables and moment generating functions
Oct. 16	MIDTERM 1
Oct. 18	Central Limit Theorem and applications
Oct. 23	Properties of the sample mean, probability inequalities
Oct. 25	Properties of point estimators, the weak law of large numbers, and confidence intervals
Oct. 30	Confidence intervals and significance testing
Nov. 1	Binary hypothesis testing
Nov. 6	Binary hypothesis testing
Nov. 8	Reliability analysis
Nov. 13	Reliability analysis and discrete time Markoc chains
Nov. 15	MIDTERM 2
Nov. 20	Discrete-time Markov chains and limiting state behavior
Nov. 27	Limiting state behavior and state classification for Markov chains
Nov. 29	Finite state Markov chains
Dec. 4	Markov Chains wiith countably infinite number of states
Dec. 6	Final review

Tufts University Department of Electrical and Computer Engineering EE-193: Applied Probability and Statistics for Engineers Fall 2007

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