Introductory Statistics

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IS: Module Three, Probability

[Module 3]
Module 3: Probability

A primary difference between statistics and mathematics is that statistics extends mathematics by understanding the effects of describable randomness on our functions. Thus, a good course in introductory statistics will have a section devoted to probability theory.

As we move through this learning module, be aware that we are trying to understand the data-generating process, the natural procedure that produces the data we wish to undestand. This is a fundamental goal of scientists. We can use logic to get close to the data-generating process. However, it is usually impossible to get it exactly. We are only able to approximate it.

This module is broken into two main sections. The fist covers discrete random variables; the second, continuous. These two types of distributions must be handled differently because of the underlying mathematical differences between discrete and continuous. However, what is produced is common between the two.

[objectives] Module Objectives

By the end of this module, the student will

  • understand the importance of independent events
  • know the differences between discrete and continuous random variables
  • know the five requirements for a Binomial distribution
  • compare and contrast Bernoulli, Binomial, and Poisson random variables
  • know the difference between pmf, pdf, and CDF
  • be able to calculate probabilities regarding a Uniform, Exponential, and Normal distribution
  • be able to calculate quantiles (percentiles)

[videos] Videos

Here are some videos that you may find helpful for mastering the material in this module.

Identifying Distributions [Identifying Distributions]

This web application gives you practice in identifying distributions and their parameters. This is an important skill to have, as it shows an understanding of the data-generating processes (and the distributions) covered in the course.

This page was last modified on 2 January 2024.
All rights reserved by Ole J. Forsberg, PhD, ©2008–2024. No reproduction of any of this material is allowed without explicit written permission of the copyright holder.