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.
Overview
Syllabus
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?.
Taught by
Iain Explains Signals, Systems, and Digital Comms
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Reviews
4.7 rating, based on 3 Class Central reviews
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AITHA SOVAN VARMAThis teaching video excels in its clarity and engaging presentation style. The instructor effectively communicates complex concepts with simplicity, making it accessible to viewers. Visual aids are utilized masterfully, enhancing comprehension and retention. The pacing keeps the audience captivated, ensuring attention throughout. Practical examples and exercises encourage active participation, fostering deeper understanding. Overall, this video is a valuable resource for learners, providing comprehensive coverage of the topic while maintaining engagement. Highly recommended for anyone seeking to grasp the subject matter effectively and efficiently.
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2205 A41126By using this course I learnreally enjoyed the online course. I thought it was well planned and layed out, easy for me to follow. The work load(h.w. & test)was just enough, so i could finish everything with enough time, learn about the topics and not feel over loaded and rushed.
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Excellent explanation and it's so useful for us thank you sir really really this is great course and I learned keep doing free course certification sir and make more videos like this
