Overview

Dive into a comprehensive series of short videos covering essential concepts in Engineering Probability. Explore topics ranging from basic principles like experiments, sample spaces, and events to advanced subjects such as random variables, probability distributions, and estimation techniques. Learn about axioms of probability, combinatorics, conditional probability, Bayes' Rule, and various probability theorems. Delve into discrete and continuous random variables, probability mass and density functions, expected values, and variance. Examine joint probability distributions, independence, covariance, and correlation. Study the Central Limit Theorem, laws of large numbers, and confidence intervals. Gain practical skills in hypothesis testing, significance testing, and random number generation. Master key probability concepts through numerous practice problems and real-world examples, including the Monty Hall problem and medical testing scenarios.

Syllabus

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.