probability
- the set of outcomes is the sample space
- the probability of an event occurring is the relative frequency of that outcome being observed
- the result of a random experiment is denoted as a random variable
- e.g., $P(X=x)
events
- a event is a subset of points in a sample space
- a probability of the event is the sum of probabilities of each sample point it contains
- e.g., $P(X>4)
- conditional probability is the probability of an event given information about some other event
distribution
- a probability distribution tracks the probabilities of random variables over the entire sample space
- for discrete variables use a probability distribution function. return a probability of an outcome being given a value (sums to 1)
- for continuous variables use a probability density function. returns the likelihood of an outcome being close to a given value (integrates to 1)
- a distribution of two or more random variables is called a joint distribution