Skip to content Skip to navigation

Connexions

You are here: Home » Content » Discrete Random Variables: Lab I

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: Lab I

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: This module allows students to explore concepts related to discrete random variables through the use of a simple playing card experiment. Students will compare empirical data to a theoretical distribution to determine if the experiment fist a discrete distribution. This lab involves the concept of long-term probabilities.

Class Time:

Names:

Student Learning Outcomes:

  • The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a discrete distribution.
  • The student will demonstrate an understanding of long-term probabilities.

Supplies:

  • One full deck of playing cards

Procedure

The experiment procedure is to pick one card from a deck of shuffled cards.

  1. The theorectical probability of picking a diamond from a deck is:
  2. Shuffle a deck of cards.
  3. Pick one card from it.
  4. Record whether it was a diamon or not a diamond.
  5. Put the card back and reshuffle.
  6. Do this a total of 10 times
  7. Record the number of diamonds picked.
  8. Let X=X= number of diamonds. Theoretically, XX ~

Organize the Data

  1. Record the number of diamonds picked for your class in the chart below. Then calculate the relative frequency.
    X Frequency Relative Frequency
    0 __________ __________
    1 __________ __________
    2 __________ __________
    3 __________ __________
    4 __________ __________
    5 __________ __________
    6 __________ __________
    7 __________ __________
    8 __________ __________
    9 __________ __________
    10 __________ __________
  2. Calculate the following:
    • a. x¯ x =
    • b. ss =
  3. Construct a histogram of the empirical data.
    Figure 1
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Theorectical Distribution

  1. Build the theoretical PDF chart for X based on the distribution in the section above.
    X X size 12{X} {} P X = x P X = x size 12{P left (X=x right )} {}
    0  
    1  
    2  
    3  
    4  
    5  
    6  
    7  
    8  
    9  
    10  
  2. Calculate the following:
    • a. μ=μ= size 12{μ={}} {}________________________
    • b. σ=σ= size 12{σ={}} {}________________________
  3. Constuct a histogram of the theoretical distribution.
    Figure 2
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Using the Data

Calculate the following, rounding to 4 decimal places:

Note:

RF = relative frequency

Use the table from the section titled "Using the Data" here:

  • P ( X = 3 = P(X=3=
  • P ( 1 < X < 4 ) = P(1<X<4)=
  • P ( X ≥ 8 = P(X≥8=

Use the data from the section titled "Organize the Data" here:

  • RF ( X = 3 ) = RF(X=3)=
  • RF ( 1 < X < 4 ) = RF(1<X<4)=
  • RF ( X ≥ 8 ) = RF(X≥8)=

Discussion Questions

  1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences. (Note: These answers may vary and still be correct.)
  2. Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions. (Note: These answers may vary and still be correct.)
  3. Does it appear that the data fit the distribution in Part I? In 1 - 3 complete sentences, explain why or why not.
  4. Suppose that the experiment had been repeated 500 times. Which chart (from Part II or Part III) would you expect to change? Why? Why wouldn’t the other chart change? How might the chart change?

Comments, questions, feedback, criticisms?

Send feedback