Review for Test #1
- Basic Probability Concepts
- sample space, events, independence
- conditional probabilities
- Bayes' formula
- Random Variables
- standard distributions (Bernoulli, binomial, geometric, Poisson, uniform, exponential, gamma)
- expected value, variance, covariance
- sums of independent random variables
- moments, moment generating function
- joint distributions, marginal distributions
- conditional distributions, conditional means
- using conditioning to find expected value, variance
- Markov Chains
- examples, formulation of models
- transition probabilities, state transition diagram
- higher-order transition probabilities
- absolute probabilities
- classification of states (recurrent, transient, periodic)
- limiting probabilities
- stationary probabilities