Wiki Page, Math 13 - Perez Sandbox : Module 11 - Wrap Up "Probability and Probability Distributions"

Wiki Page
2026-01-17T21:15:11-08:00

Let’s Summarize

The probability of an event is a measure of the likelihood that the event occurs.

Probabilities are always between 0 and 1. The closer the probability is to 0, the less likely the event is to occur. The closer the probability is to 1, the more likely the event is to occur.

The two ways of determining probabilities are empirical and theoretical.

Empirical methods use data from a series of trials. The probability of an outcome is approximated by the relative frequency of the outcome (# times the outcome occurs/ # trials).

Theoretical methods do not use data.

An empirical probability can be an estimate for a theoretical probability.

A probability distribution shows the probability for each possible outcome. The sum of all of the probabilities is 1.

We can have probability distributions for a categorical variable, such as coin toss or blood type, and for a quantitative variable, such as number of eggs in a boreal owl nest or the first digit of income reported on a tax return.

If the variable is quantitative, we can describe the distribution using shape, center (mean) and spread (standard deviation).

For a quantitative variable, the mean of the probability distribution is called the expected value. It is a weighted mean, where each variable value is weighted based on its probability.

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