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Textbook by: Mary Teegarden. E-mail the author

# Discrete Random Variables: Lab I (edited: Teegarden)

Module by: Mary Teegarden. E-mail the author

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. Labs changed to incorporate mini-tabs.

Discrete Probability Lab

Name:

## 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.

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

1. The theoretical probability of picking a diamond from a deck is:
2. Shuffle a deck of cards and pick one card from it and record whether it was a diamond or not a diamond.
3. Put the card back and reshuffle.
4. Do this a total of 10 times and record the number of diamonds picked.
5. What is the experimental probability of drawing a diamond?
6. How does the experimental probability compare to the theoretical probability? (high/low/about the same)

Using Minitab, simulate this experiment (drawing a card 10 times and recording the number of diamonds) for a total of 50 times. Use Calc -> Random data -> Binomial.

## I Organize the Data:

### Summarize the data generated in Minitab and include determine both the frequency and relative frequency. Record the result here:

 X Frequency Relative Frequency 0 1 2 3 4 5 6 7 8 9 10

2. Calculate the following using Minitab. (include the session window)

x¯x¯ size 12{ {overline {x}} } {}= ________________________ s = ________________________

3. Construct a bar chart of the experimental data using the relative frequency as the vertical axis and attach it to this cover sheet. Don’t forget a title and labels for the graph

## II. Theoretical Distribution

1. Using Minitab, build the theoretical PDF chart for X based on the distribution in the section above.

 X P(X) 0 1 2 3 4 5 6 7 8 9 10

2. Calculate the following, indicating the formulas:

μ = ________________________ σ = ________________________

3. Constuct a graph of the theoretical distribution by using:

graph probability distribution plot single view Binomial

Attach the graph to this cover sheet.

## III. Using the Data

Using the Theoretical probability table generated by Minitab, determine the following theoretical probabilities, rounding to 4 decimal places:

P(X = 3) =_______________ P(2 < X < 5) = _______________ P(X > 8) _______________

Using the data from the Minitab simulation, determine the following empirical (experimental) probabilities:

P(X = 3) = _______________ P(2 < X < 5) = _______________ P(X > 8) _______________

## IV. Discussion Questions:

### Answer the following in complete sentences on a separate sheet of paper and attach it to this cover sheet.

1. Knowing that data vary, describe two similarities between the graphs and distributions of the theoretical and experimental distributions.
2. Describe the two most significant differences between the graphs or distributions of the theoretical and experimental distributions.
3. Suppose that the experiment had been repeated 500 times. Would you expect the frequency table and bar chart in part I above to change? How and Why? Repeat the experiment and justify your answer. (Be sure to include the data summary and bar chart.)

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