POPH90148 - Probability and Distribution Theory Notes

Description

This is a comprehensive compilation of information from POPH90148 lectures, the textbook, tutorials, practicals, workshops, problem booklets and other useful sources I found online to aid my study. Includes all summarised formulae required to know for each topic. Topics included are: 1. Classic probability model (set notation, events, sample space, probability of events, combinatorial methods, conditional probability, independence, law of total probability, Bayes rule) 2. Discrete random variables (random variable, Bernoulli, Binomial and Poisson distributions, hypergeometric distribution, expectation and variance of discrete RVs, moment generating functions for discrete RVs) 3. Continuous random variables (cdf and pdf, mean and variance of continuous RVs, uniform, normal and lognormal disributions, moment generating functions for continuous RVs, transformations of a RV, method of transformations) 4. Multivariate RVs (correlation, covariance, joint/conditional/marginal distributions, bivariate and multinomial distributions, condition expectation/variance, expectation/variance of transformations of multiple RVs, order statistics) 5. Estimation (parameter, estimator, estimate, sampling distributions, standard error, unbiasedness, consistency, efficiency, Central Limit Theorem, confidence intervals)