### Overview

### 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.

### Taught by

Rich Radke