Probability, Random Variables, and Probability Distributions

These flashcards cover key vocabulary terms and definitions related to probability and statistics, based on the lecture notes.

Random Model

An imitation of the real process that we can manipulate and control to simulate randomness.

Simulation

A technique that mimics reality by using random numbers to represent the outcomes of real events.

Trial

A single attempt to perform an experiment in a simulation or other random process.

Outcome

The value measured, observed, or reported for an individual instance of a trial.

Event

A collection of outcomes in a probability experiment.

Sample Space

The collection of all possible outcomes of a random experiment, denoted often by \omega (omega).

Law of Large Numbers

A principle stating that as we repeat a random process over and over, the proportion of times an event occurs settles down to a single value.

Theoretical Probability

Probability derived from a mathematical model rather than from actual observations.

Mutually Exclusive Events

Events that cannot occur at the same time, meaning they have no outcomes in common.

Complement of an Event A

The set of outcomes that are not in event A.

Empirical Probability

Probability based on observing how often an event occurs in a series of trials.

Probability Rules (Rule 1)

The probability of any event must be between 0 and 1, inclusive (0 \le P(A) \le 1).

Probability Rules (Rule 2)

The sum of the probabilities of all possible outcomes in a sample space must equal 1 (\sum P(\text{outcome}) = 1).