Probability & Randomness
Statistics
Probability
Probability foundations, random variables, distributions, and moments.
Probability provides the language for representing biological variation, sampling, and measurement uncertainty.
Foundations
- Probability spaces, events, and probability axioms
- Counting rules and combinatorial probability
- Random variables and probability distributions
- Expectation, variance, and moments
- Joint, marginal, and conditional distributions
- Independence and conditional independence
- Conditional probability and the law of total probability
- Bayes’ theorem and Bayesian updating
- Covariance and correlation
- Transformations of random variables
- Bernoulli and binomial distributions
- Categorical and multinomial distributions
- Poisson distribution and Poisson processes
- Exponential and geometric distributions
- Normal and multivariate normal distributions
- Chi-squared, Student’s t, and F distributions
- Gamma and beta distributions
- Dirichlet distribution
- Negative binomial distribution and overdispersion
- Beta-binomial distribution
- Dirichlet–multinomial distribution
- Zero-inflated and hurdle distributions
- Probability-generating and moment-generating functions
- Order statistics and extreme values
- Probability distributions