37161 Probability and Random Variables Formula/Summary Sheet

Description

Full Summary notes of all topics from weeks 1-10. Each topic is sorted by week, including the relevant formulas and key points. Topics include: Random experiments, deterministic versus stochastic systems; Interpretations of probability; Conditional probability; Mutual exclusivity; Venn diagrams; Simple set theory and de Morgan’s laws; Bayes Theorem; Hidden state models; Interpretation of signals; Discrete random variables; Probability mass functions; cumulative probability functions; Expectation and variance; Applications including fair pricing of financial options and elementary game theory; Bernoulli and Binomial distributions; convolutions; Exponential distribution and its relation to Poisson distribution; Conditional distributions and conditional expectation; Functions of random variables; Order statistics of variables; Generating functions; Sums of random variables; Discrete Markov Chains; Classification of Markov Chains, reducibility, periodicity, recurrent/transient/absorbing states.