Skip to content Skip to navigation

Connexions

You are here: Home » Content » Discrete Random Variables: Introduction

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

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

      What is in a lens?

      Lens makers point to Connexions 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 Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the authors

Lenses

What is a lens?

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to Connexions 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 Connexions member, a community, or a respected organization.

This content is ...

In these lenses

  • Printable Books

    This module is included inLens: Connexions Books Available for Print on Demand
    By: ConnexionsAs a part of collection:"Collaborative Statistics"

    Comments:

    "This book was purchased from the authors by the Maxfield Foundation and provided to the community as an open textbook available freely online and in PDF format. Bound copies of the book can also […]"

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

  • Bio 502 at CSUDH

    This module is included inLens: Bio 502
    By: Terrence McGlynnAs a part of collection:"Collaborative Statistics"

    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.

Recently Viewed

Tags

(What is a tag?)

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

Discrete Random Variables: Introduction

Module by: Dr. Barbara Illowsky, Susan Dean

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

Student Learning Objectives

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 value.
  • 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 is data that you can count. A random variable describes the outcomes of a statistical experiment both in words and numerically. 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 defined in words.

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 (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.

XX Varience of XX Relative Frequency of XX
     
     
     
     
     
     
  • Which value(s) of XX occurred most frequently?
  • If you tossed the coin 1,000 times, what values would 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 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 a number of children in a family, then domain is and xx size 12{x} {} represents any integer from 0 to 20. Variable in statistics differs from variable in intermediate algebra in two following ways.
  • The domain of random variable (RV) is not necessarily numerical set; it can be some “wording” set; for example, if XX size 12{X} {} = hair color then the domain is {black, blond, gray, green, orange}.
  • We can tell what specific value of xx size 12{x} {} does the variable XX size 12{X} {} take only after performing the experiment.
Before the experiment any value from domain is possible. For example, without ultrasound we can not tell the gender of a baby that should be delivered, but after delivery the gender is evident. More exact, every value from the domain is accompanied with some number pp size 12{p} {}, 0≤p≤10≤p≤1 size 12{0 <= p <= 1} {}, that characterizes the chance to have this value as an outcome of the experiment. In the example with gender, p=12p=12 size 12{p= { {1} over {2} } } {}. That’s why statisticians use more exact name “Random variable” (RV) instead of variable. Even more, they use word “distribution” having in the mind the RV, that is the pairing (value, probability of the value).

Comments, questions, feedback, criticisms?

Send feedback