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PB 1: Experiments and Sample Spaces
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Classroom Contents
Probability Bites
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- 1 PB 0: Introduction
- 2 PB 1: Experiments and Sample Spaces
- 3 PB 2: Events
- 4 PB 3: Axioms of Probability
- 5 PB 4: Discrete Sample Spaces
- 6 PB 5: Combinatorics
- 7 PB 6: Combinatorics Practice Problems
- 8 PB 7: Continuous Sample Spaces
- 9 PB 8: Conditional Probability
- 10 PB 9: The Total Probability Theorem
- 11 PB 10: Bayes' Rule
- 12 PB11: A Medical Testing Example
- 13 PB12: The Monty Hall Problem
- 14 PB13: Independent Events
- 15 PB14: Bernoulli Trials
- 16 PB15: Binomial and Geometric Practice Problems
- 17 PB16: Bernoulli's Theorem
- 18 PB17: Discrete Random Variables
- 19 PB18: Probability Mass Function
- 20 PB19: The Poisson Random Variable
- 21 PB20: Expected Value for Discrete Random Variables
- 22 PB21: Expected Value of Functions
- 23 PB22: The Variance
- 24 PB23: Conditional Probability Mass Functions
- 25 PB24: The Memoryless Property
- 26 PB25: Conditional Expected Value
- 27 PB26: Cumulative Distribution Functions
- 28 PB27: Continuous Random Variables
- 29 PB28: Probability Density Functions
- 30 PB29: The Exponential Random Variable
- 31 PB30: The Gaussian Random Variable
- 32 PB31: Q Function Practice Problems
- 33 PB32: Expected Value for Continuous Random Variables
- 34 PB33: Expected Value of Functions of a Random Variable
- 35 PB34: Expected Value Practice Problems (Using Integration)
- 36 PB35: Expected Value Practice Problems (Using Properties)
- 37 PB36: Designing a Quantizer
- 38 PB37: One-to-One Functions of a Random Variable
- 39 PB38: Many-to-One Functions of a Random Variable
- 40 PB39: Markov and Chebyshev Inequalities
- 41 PB40: Two Discrete Random Variables
- 42 PB41: Joint PMF/CDF for Discrete Random Variables
- 43 PB42: The Marginal PMF for Discrete Random Variables
- 44 PB43: Joint PDF/CDF and Marginals for Continuous Random Variables
- 45 PB44: Joint Random Variable Practice Problems
- 46 PB45: The Joint Gaussian Random Variable
- 47 PB46: Independence of Random Variables
- 48 PB47: Joint Expectations and Covariance
- 49 PB48: The Correlation Coefficient
- 50 PB49: Conditional PMFs for Discrete Random Variables
- 51 PB50: Class-Conditional Probability Density Functions
- 52 PB51: The Bayes Decision Rule
- 53 PB52: Conditional PDFs for Continuous Joint Random Variables
- 54 PB53: Conditional Gaussian Distributions
- 55 PB54: The Law of Iterated Expectation
- 56 PB55: Conditional Expectation Practice Problems
- 57 PB56: More Conditional Expectation Practice Problems
- 58 PB57: Sums of Random Variables
- 59 PB58: Laws of Large Numbers
- 60 PB59: The PDF of a Sum of Random Variables
- 61 PB60: Transformations of Random Variables
- 62 PB61: The Central Limit Theorem
- 63 PB62: Central Limit Theorem Practice Problems
- 64 PB63: Weak Law of Large Numbers vs. Central Limit Theorem
- 65 PB64: Confidence Intervals
- 66 PB65: Maximum A Posteriori (MAP) Estimation
- 67 PB66: Maximum Likelihood Estimation
- 68 PB67: Minimum Mean-Square Estimation
- 69 PB68: Linear Minimum Mean-Square Estimation
- 70 PB69: Significance Testing
- 71 PB70: Hypothesis Testing
- 72 PB71: A Hypothesis Testing Example
- 73 PB72: Testing the Fit of a Distribution
- 74 PB73: Generating Samples of a Random Variable
- 75 PB74: Tips and Tricks for Random Number Generation
