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# Probability Bites

### 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.

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