Engineering Probability Lectures, Fall 2018

Dive into a comprehensive lecture series on Engineering Probability, delivered by Rich Radke at Rensselaer Polytechnic Institute. Explore fundamental concepts such as sample spaces, events, axioms of probability, and counting methods before progressing to more advanced topics including discrete and continuous random variables, probability density functions, and the Gaussian distribution. Learn about joint expectations, correlation, covariance, and delve into estimation techniques like Bayesian and maximum likelihood. Examine the Central Limit Theorem, hypothesis testing, and methods for generating random samples. This 22-hour course closely follows Alberto Leon-Garcia's textbook "Probability, Statistics, and Random Processes for Electrical Engineering" and provides a solid foundation in probability theory essential for engineering applications.

Engineering Probability Lecture 1: Experiments, Sample Spaces, and Events.
Engineering Probability Lecture 2: Axioms of probability and counting methods.
Engineering Probability Lecture 3: Conditional probability.
Engineering Probability Lecture 4: Independent events and Bernoulli trials.
Engineering Probability Lecture 5: Discrete random variables.
Engineering Probability Lecture 6: Expected value and moments.
Engineering Probability Lecture 7: Conditional probability mass functions.
Engineering Probability Lecture 8: Cumulative distribution functions (CDFs).
Engineering Probability Lecture 9: Probability density functions and continuous random variables.
Engineering Probability Lecture 10: The Gaussian random variable and Q function.
Engineering Probability Lecture 11: Expected value for continuous random variables.
Engineering Probability Lecture 12: Functions of a random variable; inequalities.
Engineering Probability Lecture 13: Two random variables (discrete).
Engineering Probability Lecture 14: Two random variables (continuous); independence.
Engineering Probability Lecture 15: Joint expectations; correlation and covariance.
Engineering Probability Lecture 16: Conditional PDFs; Bayesian and maximum likelihood estimation.
Engineering Probability Lecture 17: Conditional expectations.
Engineering Probability Lecture 18: Sums of random variables and laws of large numbers.
Engineering Probability Lecture 19: The Central Limit Theorem.
Engineering Probability Lecture 20: MAP, ML, and MMSE estimation.
Engineering Probability Lecture 21: Hypothesis testing.
Engineering Probability Lecture 22: Testing the fit of a distribution; generating random samples.