Probability

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• From counting to a measure ~10 min
• The three axioms ~11 min
• Monotonicity and the complement rule ~10 min
• Probability of a union, two events ~10 min
• Inclusion-exclusion, three events ~10 min
• De Morgan's laws for events ~9 min
• Equally likely outcomes, revisited ~9 min
• Empirical versus theoretical probability ~9 min
• The law of large numbers: a first look ~9 min
• Common probability fallacies ~10 min

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• Review — the product and sum rules ~8 min
• Review — permutations and combinations ~8 min
• Permutations with repeated objects ~9 min
• Circular permutations ~8 min
• Multinomial coefficients ~9 min
• Counting with restrictions ~9 min
• Complementary counting ~8 min
• Stars and bars ~9 min
• Choosing a counting method ~10 min

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• Conditioning as a restricted sample space ~11 min
• The multiplication rule ~10 min
• The law of total probability ~11 min
• Tree diagrams for sequential experiments ~10 min
• Bayes' theorem ~12 min
• Prior, likelihood, and posterior ~9 min
• Bayes in odds form ~10 min
• Base rates and the prosecutor's fallacy ~10 min
• Independent events ~10 min
• Pairwise versus mutual independence ~10 min

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• What a random variable is ~10 min
• Discrete versus continuous: a first look ~8 min
• The probability mass function ~9 min
• What makes a pmf valid ~8 min
• Computing event probabilities from a pmf ~9 min
• The cumulative distribution function ~9 min
• Properties of a discrete CDF ~8 min
• Reading a CDF graph ~8 min
• Indicator random variables ~8 min

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• Expected value from a pmf ~9 min
• Expected value: the long-run average interpretation ~8 min
• Expected value of a function of X (LOTUS) ~9 min
• Linearity of expectation ~8 min
• The indicator trick ~9 min
• Variance, defined ~9 min
• The computational formula for variance ~8 min
• Standard deviation and units ~8 min
• Variance under scaling ~8 min
• Sums of independent variables ~9 min
• Games of chance and expected winnings ~9 min

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• The Bernoulli distribution ~8 min
• The binomial distribution ~9 min
• The geometric distribution ~8 min
• The memoryless property, discretely ~7 min
• The negative binomial distribution ~8 min
• The hypergeometric distribution ~9 min
• The Poisson distribution ~9 min
• Poisson as a limit of binomial ~8 min
• The discrete uniform distribution ~7 min
• Choosing a discrete model ~9 min

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• From mass to density ~8 min
• Why P(X=x)=0 ~7 min
• The probability density function ~8 min
• What makes a pdf valid ~7 min
• Probability as area ~8 min
• The continuous CDF ~8 min
• The derivative/integral relationship ~7 min
• Quantiles and the median ~8 min
• Expectation for a continuous variable ~8 min

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• The continuous uniform distribution ~7 min
• The exponential distribution ~8 min
• Memorylessness, continuously ~7 min
• The normal distribution ~8 min
• The standard normal distribution ~7 min
• Z-scores and standardization ~8 min
• The empirical rule ~7 min
• Normal approximation to the binomial ~8 min
• The continuity correction ~8 min
• Choosing a continuous model ~8 min

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• Two random variables at once ~7 min
• Joint probability mass functions ~8 min
• Joint probability density functions ~8 min
• Marginal distributions ~8 min
• Conditional distributions ~8 min
• Conditional expectation ~8 min
• Independence of random variables ~8 min
• Covariance ~8 min
• Correlation ~8 min
• Correlation versus causation ~7 min

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• Functions of a random variable ~7 min
• Linear transformations, Y=aX+b ~7 min
• Mean under a linear transformation ~7 min
• Variance under a linear transformation ~7 min
• Standardization, revisited ~7 min
• The CDF method for a transformed variable ~8 min
• Sums of independent random variables ~8 min

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• The sample average as a random variable ~8 min
• Chebyshev's inequality ~8 min
• The weak law of large numbers ~8 min
• Why probability doesn't "balance out" immediately ~7 min
• The gambler's fallacy ~7 min
• Standard error ~7 min
• The central limit theorem ~9 min
• Conditions and failures of the CLT ~8 min
• Using the CLT to approximate a probability ~8 min

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• Population versus sample ~7 min
• Sampling with replacement ~7 min
• Sampling without replacement ~7 min
• The finite population correction ~8 min
• The sampling distribution of a proportion ~8 min
• The sampling distribution of a mean ~7 min
• The sampling distribution of a variance, previewed ~6 min
• Where probability ends and statistics begins ~7 min

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• The Monty Hall problem ~7 min
• The birthday problem ~7 min
• Gambler's ruin ~8 min
• Random walks ~7 min
• Reliability of series and parallel systems ~8 min
• Queues, a first look ~7 min
• Naive Bayes spam filtering ~7 min
• A/B testing and risk ~7 min
• Monte Carlo simulation as a method ~8 min