Ali Tajer
Associate Professor
Electrical, Computer, and Systems Engineering
Rensselaer Polytechnic Institute
(518) 2768237
6040 Jonsson Engineering Center, 110 8th Street, Troy, NY 12180
Engineering Probability
Fall 2021
Title  Topic 

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  Probability distribution functions, continuous random variables 
Lecture 10  The Gaussian random variable, Q function 
Lecture 11  Expectations of a random variable 
Lecture 12  Functions of a random variable; inequalities 
Lecture 13  Two random variables (discrete) 
Lecture 14  Two random variables (continuous); independence 
Lecture 15  Joint expectations, correlation, covariance 
Lecture 16  Conditional PDFs; Bayesian and maximum likelihood estimation 
Lecture 17  Conditional expectations 
Lecture 18  Sums of random variables 
Lecture 19  Sums of random variables 
Lecture 20  Central limit theorem; confidence intervals 
Lecture 21  MAP, ML, and MMSE estimation 
Lecture 22  Hypothesis testing 
Lecture 23  Testing the fitness of a distribution; generating random samples 