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Discrete Random Variables: Practice 4: Geometric Distribution

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

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Summary: This module provides further practice with topics of Geometric Distribution in Statistics.

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Student Learning Objectives

  • The student will investigate the properties of a geometric distribution.

Given:

Use the information from the Binomial Distribution Practice. Suppose that you will randomly select one freshman from the study until you find one who expects to work full-time while in college. You are interested in the number of freshmen you must ask.

Interpret the Data

Exercise 1

In words, define the Random Variable XX.

Exercise 2

XX ~

Solution

G(0.367)

Exercise 3

What values does X X take on?

Solution

0,1,2,…

Exercise 4

Construct the probability distribution function (PDF) for XX. Stop at X = 6X=6.

Table 1
xx P(X=x)P(X=x)
0  
1  
2  
3  
4  
5  
6  

Exercise 5

On average(μμ), how many freshmen would you expect to have to ask until you found one who expects to work full-time while in college?

Solution

2.72

Exercise 6

What is the probability that you will need to ask fewer than 3 freshmen?

Solution

0.5993

Exercise 7

Construct a histogram or plot a line graph. Label the horizontal and vertical axes with words. Include numerical scaling.

Blank graph with vertical and horizontal axes.

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