Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Collaborative Statistics » Discrete Random Variables

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This collection is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook Collaborative

    Comments:

    "Reviewer's Comments: 'I recommend this book. Overall, the chapters are very readable and the material presented is consistent and appropriate for the course. A wide range of exercises introduces […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This collection is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange Grove

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "Collaborative Statistics was written by two faculty members at De Anza College in Cupertino, California. This book is intended for introductory statistics courses being taken by students at two- […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lucy Van Pelt display tagshide tags

    This collection is included inLens: Lucy's Lens
    By: Tahiya Marome

    Comments:

    "Part of the Books featured on Community College Open Textbook Project"

    Click the "Lucy Van Pelt" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

  • Educational Technology Lens display tagshide tags

    This collection is included inLens: Educational Technology
    By: Steve Wilhite

    Click the "Educational Technology Lens" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

  • crowe

    This collection is included in aLens by: Chris Rowe

    Click the "crowe" link to see all content selected in this lens.

  • Bio 502 at CSUDH display tagshide tags

    This collection is included inLens: Bio 502
    By: Terrence McGlynn

    Comments:

    "This is the course textbook for Biology 502 at CSU Dominguez Hills"

    Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Discrete Random Variables

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module serves as the introduction to Discrete Random Variables in the Elementary Statistics textbook/collection.

Student Learning Outcomes

By the end of this chapter, the student should be able to:

  • Recognize and understand discrete probability distribution functions, in general.
  • Calculate and interpret expected values.
  • Recognize the binomial probability distribution and apply it appropriately.
  • Recognize the Poisson probability distribution and apply it appropriately (optional).
  • Recognize the geometric probability distribution and apply it appropriately (optional).
  • Recognize the hypergeometric probability distribution and apply it appropriately (optional).
  • Classify discrete word problems by their distributions.

Introduction

A student takes a 10 question true-false quiz. Because the student had such a busy schedule, he or she could not study and randomly guesses at each answer. What is the probability of the student passing the test with at least a 70%?

Small companies might be interested in the number of long distance phone calls their employees make during the peak time of the day. Suppose the average is 20 calls. What is the probability that the employees make more than 20 long distance phone calls during the peak time?

These two examples illustrate two different types of probability problems involving discrete random variables. Recall that discrete data are data that you can count. A random variable describes the outcomes of a statistical experiment in words. The values of a random variable can vary with each repetition of an experiment.

In this chapter, you will study probability problems involving discrete random distributions. You will also study long-term averages associated with them.

Random Variable Notation

Upper case letters like XX or YY denote a random variable. Lower case letters like xx or yy denote the value of a random variable. If XX is a random variable, then XX is written in words. and xx is given as a number.

For example, let XX = the number of heads you get when you toss three fair coins. The sample space for the toss of three fair coins is TTTTTT; THHTHH; HTHHTH; HHT HHT; HTTHTT; THTTHT; TTHTTH; HHH HHH. Then, xx = 0, 1, 2, 3. XX is in words and xx is a number. Notice that for this example, the xx values are countable outcomes. Because you can count the possible values that XX can take on and the outcomes are random (the xx values 0, 1, 2, 3), XX is a discrete random variable.

Optional Collaborative Classroom Activity

Toss a coin 10 times and record the number of heads. After all members of the class have completed the experiment (tossed a coin 10 times and counted the number of heads), fill in the chart using a heading like the one below. Let XX = the number of heads in 10 tosses of the coin.

Table 1
xx Frequency of xx Relative Frequency of xx
     
     
     
     
     
     
  • Which value(s) of xx occurred most frequently?
  • If you tossed the coin 1,000 times, what values could xx take on? Which value(s) of xx do you think would occur most frequently?
  • What does the relative frequency column sum to?

Glossary

Random Variable (RV):
see Variable
Variable (Random Variable):
A characteristic of interest in a population being studied. Common notation for variables are upper case Latin letters XX size 12{X} {}, YY size 12{Y} {}, ZZ size 12{Z} {},...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters xx size 12{x} {}, yy size 12{y} {}, zz size 12{z} {},.... For example, if XX size 12{X} {} is the number of children in a family, then xx size 12{x} {} represents a specific integer 0, 1, 2, 3, .... Variables in statistics differ from variables in intermediate algebra in two following ways.
  • The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if XX size 12{X} {} = hair color then the domain is {black, blond, gray, green, orange}.
  • We can tell what specific value xx size 12{x} {} of the Random Variable XX size 12{X} {} takes only after performing the experiment.

Collection Navigation

Content actions

Download module as:

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks