Probability and Random Processes

Dive into a comprehensive video series exploring the fundamentals of probability theory and random processes. Learn about random variables, probability density functions, and cumulative distribution functions with intuitive explanations. Discover key concepts like Gaussian and Chi-Square distributions, expectation of random variables, and the Central Limit Theorem. Explore random processes, autocorrelation, and power spectral density with examples from digital communications. Gain insights into parameter estimation techniques such as Maximum Likelihood and Maximum a posteriori. Understand important statistical tests, including the Pearson Chi-Square test, and delve into advanced topics like Wide Sense Stationarity, Moment Generating Functions, and the Chernoff Bound. Unravel the relationships between error functions, Q-functions, and Gaussian tails. Tackle interesting problems like the Three Door Gameshow and explore characteristic functions, least squares estimation, Poisson processes, and conditional probability. Perfect for students, professionals, and enthusiasts seeking a deep understanding of probability and random processes in just over 3 hours.

What is a Random Variable?.
What is a Probability Density Function (pdf)? ("by far the best and easy to understand explanation").
What is a Cumulative Distribution Function (CDF) of a Random Variable?.
Expectation of a Random Variable Equation Explained.
What is a Gaussian Distribution?.
What is a Chi Square Distribution? with examples.
What is a Random Process?.
Autocorrelation and Power Spectral Density (PSD) Examples in Digital Communications.
What is the Central Limit Theorem?.
What are Maximum Likelihood (ML) and Maximum a posteriori (MAP)? ("Best explanation on YouTube").
Testing Random Data Models: Pearson Chi Square Test.
What does Wide Sense Stationary (WSS) mean?.
What is a Moment Generating Function (MGF)? ("Best explanation on YouTube").
What is the Chernoff Bound?.
How are erf(.), Q(.), and Gaussian Tails Related?.
Three Door Gameshow Problem Explained.
What is the Characteristic Function of a Random Variable?.
Moment Generating Function of a Gaussian.
What is Least Squares Estimation?.
What is a Poisson Process?.
What is Conditional Probability?.