In Summer 2022 I created this set of short (roughly 10-minute each) lectures for my Engineering Probability (ECSE-2500) class at Rensselaer Polytechnic Institute. They loosely accompany Probability, Statistics, and Random Processes for Electrical Engineering, 3rd edition, by Alberto Leon-Garcia, Prentice Hall, 2008.

You may also be interested in my annotated course lectures for Digital Signal Processing, Introduction to Image Processing, and Computer Vision for Visual Effects. I also have roughly hour-long lectures on Engineering Probability at this link, but I think these short lectures are better.

PB 0: Introduction



PB 1: Experiments and Sample Spaces



PB 2: Events



PB 3: Axioms of Probability



PB 4: Discrete Sample Spaces



PB 5: Combinatorics



PB 6: Combinatorics Practice Problems



PB 7: Continuous Sample Spaces



PB 8: Conditional Probability



PB 9: The Total Probability Theorem



PB 10: Bayes' Rule



PB11: A Medical Testing Example



PB12: The Monty Hall Problem



PB13: Independent Events



PB14: Bernoulli Trials



PB15: Binomial and Geometric Practice Problems



PB16: Bernoulli's Theorem



PB17: Discrete Random Variables



PB18: Probability Mass Function



PB19: The Poisson Random Variable



PB20: Expected Value for Discrete Random Variables



PB21: Expected Value of Functions



PB22: The Variance



PB23: Conditional Probability Mass Functions



PB24: The Memoryless Property



PB25: Conditional Expected Value



PB26: Cumulative Distribution Functions



PB27: Continuous Random Variables



PB28: Probability Density Functions



PB29: The Exponential Random Variable



PB30: The Gaussian Random Variable



PB31: Q Function Practice Problems



PB32: Expected Value for Continuous Random Variables



PB33: Expected Value of Functions of a Random Variable



PB34: Expected Value Practice Problems (Using Integration)



PB35: Expected Value Practice Problems (Using Properties)



PB36: Designing a Quantizer



PB37: One-to-One Functions of a Random Variable



PB38: Many-to-One Functions of a Random Variable



PB39: Markov and Chebyshev Inequalities



PB40: Two Discrete Random Variables



PB41: Joint PMF/CDF for Discrete Random Variables



PB42: The Marginal PMF for Discrete Random Variables



PB43: Joint PDF/CDF and Marginals for Continuous Random Variables



PB44: Joint Random Variable Practice Problems



PB45: The Joint Gaussian Random Variable



PB46: Independence of Random Variables



PB47: Joint Expectations and Covariance



PB48: The Correlation Coefficient



PB49: Conditional PMFs for Discrete Random Variables



PB50: Class-Conditional Probability Density Functions



PB51: The Bayes Decision Rule



PB52: Conditional PDFs for Continuous Joint Random Variables



PB53: Conditional Gaussian Distributions



PB54: The Law of Iterated Expectation



PB55: Conditional Expectation Practice Problems



PB56: More Conditional Expectation Practice Problems



PB57: Sums of Random Variables



PB58: Laws of Large Numbers



PB59: The PDF of a Sum of Random Variables



PB60: Transformations of Random Variables



PB61: The Central Limit Theorem



PB62: Central Limit Theorem Practice Problems



PB63: Weak Law of Large Numbers vs. Central Limit Theorem



PB64: Confidence Intervals



PB65: Maximum A Posteriori (MAP) Estimation



PB66: Maximum Likelihood Estimation



PB67: Minimum Mean-Square Estimation



PB68: Linear Minimum Mean-Square Estimation



PB69: Significance Testing



PB70: Hypothesis Testing



PB71: A Hypothesis Testing Example



PB72: Testing the Fit of a Distribution



PB73: Generating Samples of a Random Variable



PB74: Tips and Tricks for Random Number Generation



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Engineering Probability by Rich Radke is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Based on a work at http://www.ecse.rpi.edu/~rjradke/probcourse.html.
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