Statistical Analysis/Unit 3 Navigation

This is the main navigation page for Unit 3 of the course Introduction to Statistical Analysis, developed using openly licensed materials from Saylor.org's Introduction to Statistics. Below you will find a full description of Unit 3 in general, as well as for each subunit. Follow the links within each subunit description to access particular topics, or proceed directly to the Unit 3 Content Page.

UNIT 3: RANDOM VARIABLES AND DISTRIBUTIONS

In the last unit, you learned how to calculate probabilities in the framework of sample spaces, outcomes, and events. In this unit, you will build on those ideas and learn about random variables. A random variable describes the outcomes of a statistical experiment. A statistical distribution describes the numbers of times each possible outcome occurs in a sample. The values of a random variable can vary with each repetition of an experiment. Intuitively, a random variable is an observable that takes on values with certain probabilities.

A random variable can be classified as being either discrete or continuous depending on the values it assumes. Suppose you count the number of people who go to a coffee shop between 4pm and 5pm and the amount of money that they spend in that hour. In this case, the number of people is an example of a discrete random variable and the amount of money they spend is an example of a continuous random variable. In this unit, you will study probability problems involving random distributions. You will also learn about both discrete and continuous random variables and their applications. Finally, you will study an important example of a continuous distribution, the normal distribution, which is a bell-shaped distribution used widely in almost all disciplines.

A note from the book: “The values of discrete and continuous random variables can be ambiguous. For example, if X is equal to the number of miles (to the nearest mile) you drive to work, then X is a discrete random variable. You count the miles. If X is the distance you drive to work, then you measure values of X and X is a continuous random variable. How the random variable is defined is very important.”

Time Advisory

Time Advisory: This unit will take you 18 hours to complete.

• Subunit 3.1: 6 hours
• Subunit 3.2: 6 hours
• Subunit 3.3: 6 hours

Learning Outcomes

Upon completion of this this unit, you will be able to:

• Recognize and understand discrete probability distribution functions.
• Calculate and interpret expected values.
• Recognize the binomial probability distribution and apply it appropriately.
• Recognize the Poisson probability distribution and apply it appropriately.
• Recognize the geometric probability distribution and apply it appropriately.
• Recognize the hypergeometric probability distribution and apply it appropriately.
• Classify discrete word problems by their distributions.
• Recognize and understand continuous probability density functions in general.
• Recognize the uniform probability distribution and apply it appropriately.
• Recognize the exponential probability distribution and apply it appropriately.
• Recognize the normal probability distribution and apply it appropriately.
• Recognize the standard normal probability distribution and apply it appropriately.
• Compare normal probabilities by converting to the standard normal distribution.

Subunits

Unit two consists of three main topics:

Discrete Random Variables and Discrete Probability Distributions

This topic will introduce you the major concepts fundamental to probability and the terminology associated with them.

• 3.1.1: Probability Distribution Functions
• 3.1.2: Expected Value and Standard Deviation
• 3.1.3: Common Discrete Probability Distributions

Continuous Random Variables

• 3.2.1: Continuous Probability Functions
• 3.2.1: Uniform Distribution
• 3.2.1: Exponential Distribution

Normal Distribution

• 3.3.1: The Standard Normal Distribution
• 3.3.1: Z-scores
• 3.3.1: Areas to the Left and Right of x

About the Resources in This Course

This course project draws upon three main types of resources:

The first are readings and video lectures from Barbara Illowsky and Susan Dean’s Collaborative Statistics, which is available freely under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license from the following location: http://cnx.org/content/col10522/latest/

The second type of resources in this course are lectures from Kahn Academy. These lectures are available under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) license. Kahn Academy has many lectures available from http://www.khanacademy.org/

Finally, the above resources have been woven together and organized into a format analogous to a traditional college-level course by professional consultants that work as experts within the subject area. This process was facilitated by The Saylor Foundation. Additionally, if you have worked through all of the material contained in this project, you may be interested in taking the final exam provided by Saylor.org or completing other courses available there that are not yet on Wikiversity.