## Ali Tajer

## Associate Professor

## Electrical, Computer, and Systems Engineering

## Rensselaer Polytechnic Institute

##

(518) 276-8237

6040 Jonsson Engineering Center, 110 8th Street, Troy, NY 12180

## Engineering Probability

Fall 2021

__Lecture 1__

experiments, sample space, events

__Lecture 2__

axioms, probabilistic models, counting methods

__Lecture 3__

Conditional probability

__Lecture 4__

Baye's rule, independence, Bernoulli trials

__Lecture 5__

Discrete random variables

__Lecture 6__

Expected value and moments

__Lecture 7__

Conditional probability mass functions

__Lecture 8__

Cumulative distribution functions

__Lecture 9__

__Lecture 10__

Probability distribution functions, continuous random variables

__Lecture 11__

The Gaussian random variable, Q function

__Lecture 12__

Expectations of a random variable

__Lecture 13__

Functions of a random variable; inequalities

__Lecture 14__

Two random variables (discrete)

__Lecture 15__

Two random variables (continuous); independence

__Lecture 16__

Joint expectations, correlation, covariance

__Lecture 17__

Conditional PDFs; Bayesian and maximum likelihood estimation

__Lecture 18__

__Lecture 19__

Conditional expectations

__Lecture 20__

Sums of random variables

__Lecture 21__

Central limit theorem; confidence intervals

__Lecture 22__

MAP, ML, and MMSE estimation

__Lecture 23__

Hypothesis testing

__Lecture 24__

Testing the fit of a distribution; generating random samples

__Lecture 25__

TBD

__Lecture 26__

TBD