Statistics and Probability -- Part One

Random Variable

A function that assigns a number to each outcome in the sample space of an experiment.

Expected Value

The average value of the outcomes in a given experiment.

What happens to the average result of an outcome over time as more trials increase of an experiment?

It approaches the expected value of the outcome.

Mutually Exclusive Events

Two events that cannot occur at the same time, leading to a probability of 0 if both events occur.

Example of a Mutually Exclusive Event

A dice roll yielding 1 and 4. A coin flip resulting in heads and tails.

Independent Event

The occurrence of one event does not influence the probability of another event, leading to independence.

Example of an Independent Event

A fair dice is rolled twice without any change in the probability of an event.