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Discrete Random Variables: Lab I

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

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. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Note: You are viewing an old version of this document. The latest version is available here.

Class Time:


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.


  • One full deck of playing cards

Do the Experiment:

    • The experiment is to pick one card from a deck of shuffled cards.
    • The theoretical probability of picking a diamond from a deck is: _______
    • Shuffle a deck of cards. Pick one card from it. Record whether it was a diamond or not a diamond. Put the card back and reshuffle. Do this a total of 10 times. Record the number of diamonds picked: _______
    • Let XX size 12{X} {} = number of diamonds. Theoretically, X~X~ size 12{X "~" } {} ­­­_____________
  1. Record the number of diamonds picked for your class in the chart below. Then calculate the relative frequency.
    Table 1
    X X size 12{X} {} frequency   relative frequency
    • x¯=x¯= size 12{ {overline {x}} ={}} {} ­­
    • s=s= size 12{s={}} {}
  2. Construct a histogram of the empirical data.
    Figure 1
    Figure 1 (graph1.PNG)
  3. Build the theoretical PDF chart for X based on the distribution in Part I.
    Table 2
    X X size 12{X} {} P X = x P X = x size 12{P left (X=x right )} {}
    • μ=μ= size 12{μ={}} {}
    • σ=σ= size 12{σ={}} {}
  4. Construct a histogram of the theoretical distribution.
    Figure 2
    Figure 2 (graph2.PNG)
  5. Calculate the following, rounding to 4 decimal places:

    Use Part III here:

    • P X = 3 = P X = 3 = size 12{P left (X=3 right )={}} {}
    • P 1 < X < 4 = P 1 < X < 4 = size 12{P left (1<X<4 right )={}} {}
    • P X 8 = P X 8 = size 12{P left (X >= 8 right )={}} {}


    RFRF size 12{ ital "RF"} {}= relative frequency

    Use Part II here:

    • RF X = 3 = RF X = 3 = size 12{ ital "RF" left (X=3 right )={}} {}
    • RF 1 < X < 4 = RF 1 < X < 4 = size 12{ ital "RF" left (1<X<4 right )={}} {}
    • RF X 8 = RF X 8 = size 12{ ital "RF" left (X >= 8 right )={}} {}
  6. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences.


    These answers may vary and still be correct.
  7. Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions.


    These answers may vary and still be correct.
  8. Does it appear that the data fit the distribution in Part 1? In 1 - 3 complete sentences, explain why or why not.
  9. Suppose that the experiment had been repeated 500 times. Which chart (from Part 2 or Part 4) would you expect to change? Why? Why wouldn’t the other chart change? How might the chart change?

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