Probability and Distributions
Discrete and continuous random variables, and testing goodness of fit.
01ProbabilitySample spaces and equally likely outcomes, using permutations and combinations to count them, the addition and multiplication rules, reading conditional probabilities from a two-way table, multi-stage tree diagrams, and the law of total probability with Bayes' theorem.100 questions02Discrete Random VariablesThe named discrete distributions — geometric and Poisson — their formulae, means and variances, adding independent Poisson variables, scaling the interval, using the Poisson as an approximation to the binomial, and choosing the right model for a situation.100 questions03Continuous Random VariablesProbability density functions and the conditions they satisfy, finding an unknown constant, expectation and variance by integration, the cumulative distribution function, medians and quartiles, and the continuous uniform and exponential distributions.100 questions04Chi-Squared Goodness of FitTesting whether data follows a stated distribution — equal proportions, a given ratio, a binomial or a Poisson — computing expected frequencies, choosing degrees of freedom when parameters are estimated, pooling small classes, and stating the conclusion.100 questions