Probability 1 for statisticians

Basic combinatorics

• Sample space and events. Probability mass function
• Conditional probability. Law of total probability. Bayes? formula
• Independence
• Useful discrete distributions: uniform, binomial, geometric, Poisson, hypergeometric, negative binomial.
• Expectation, variance, median, percentile
• Functions of a random variable
• Two dimensional distributions: joint distribution, marginal distribution, covariance, conditioning on marginals
• Markov, Chebychev and Jensen inequalities
• Normal distribution
• Sequences of random variables: law of large numbers and central limit theorem