modeling discrete variables n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Modeling Discrete Variables PowerPoint Presentation
Download Presentation
Modeling Discrete Variables

Loading in 2 Seconds...

play fullscreen
1 / 21

Modeling Discrete Variables - PowerPoint PPT Presentation


  • 70 Views
  • Uploaded on

Modeling Discrete Variables. Lecture 22-1 Sections 6.4 Wed, Mar 1, 2006. Two Types of Variable. Discrete variable – A variable whose set of possible values is a set of isolated points on the number line.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Modeling Discrete Variables' - lucine


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
modeling discrete variables

Modeling Discrete Variables

Lecture 22-1

Sections 6.4

Wed, Mar 1, 2006

two types of variable
Two Types of Variable
  • Discrete variable – A variable whose set of possible values is a set of isolated points on the number line.
  • Continuous variable – A variable whose set of possible values is a continuous interval of real numbers.
example of a discrete variable
Example of a Discrete Variable
  • Suppose that 10% of all households have no children, 30% have one child, 40% have two children, and 20% have three children.
  • Select a household at random and let X = number of children.
  • What is the distribution of X?
example of a discrete variable1
Example of a Discrete Variable
  • We may list each value and its proportion.
    • For 0.10 of the population, X = 0.
    • For 0.30 of the population, X = 1.
    • For 0.40 of the population, X = 2.
    • For 0.20 of the population, X = 3.
example of a discrete variable2
Example of a Discrete Variable
  • Or we may present it as a table.
graphing a discrete variable
Graphing a Discrete Variable
  • Or we may present it as a stick graph.

P(X = x)

0.40

0.30

0.20

0.10

x

0

1

2

3

graphing a discrete variable1
Graphing a Discrete Variable
  • Or we may present it as a histogram.

P(X = x)

0.40

0.30

0.20

0.10

x

0

1

2

3

discrete random variables

Discrete Random Variables

Lecture 22-2

Section 7.5.1

Wed, Mar 1, 2006

random variables
Random Variables
  • Random variable – A variable whose value is determined by the outcome of a procedure.
  • The procedure includes at least one step whose outcome is left to chance.
  • Therefore, the random variable takes on a new value each time the procedure is performed, even though the procedure is exactly the same.
types of random variables
Types of Random Variables
  • Discrete Random Variable – A random variable whose set of possible values is a discrete set.
  • Continuous Random Variable – A random variable whose set of possible values is a continuous set.
a note about probability
A Note About Probability
  • The probability that something happens is the proportion of the time that it does happen out of all the times it was given an opportunity to happen.
  • Therefore, “probability” and “proportion” are synonymous in the context of what we are doing.
examples of random variables
Examples of Random Variables
  • Roll two dice. Let X be the number of sixes.
    • Possible values of X = {0, 1, 2}.
  • Roll two dice. Let X be the total of the two numbers.
    • Possible values of X = {2, 3, 4, …, 12}.
  • Select a person at random and give him up to one hour to perform a simple task. Let X be the time it takes him to perform the task.
    • Possible values of X are {x | 0 ≤ x ≤ 1}.
discrete probability distribution functions
Discrete Probability Distribution Functions
  • Discrete Probability Distribution Function (pdf) – A function that assigns a probability to each possible value of a discrete random variable.
rolling two dice
Rolling Two Dice
  • Roll two dice and let X be the number of sixes.
  • Draw the 6  6 rectangle showing all 36 possibilities.
  • From it we see that
    • P(X = 0) = 25/36.
    • P(X = 1) = 10/36.
    • P(X = 2) = 1/36.
rolling two dice1
Rolling Two Dice
  • We can summarize this in a table.
example of a discrete pdf
Example of a Discrete PDF
  • Or we may present it as a stick graph.

P(X = x)

30/36

25/36

20/36

15/36

10/36

5/36

x

0

1

2

example of a discrete pdf1
Example of a Discrete PDF
  • Or we may present it as a histogram.

P(X = x)

30/36

25/36

20/36

15/36

10/36

5/36

x

0

1

2

example of a discrete pdf2
Example of a Discrete PDF
  • Suppose that 10% of all households have no children, 30% have one child, 40% have two children, and 20% have three children.
  • Select a household at random and let X = number of children.
  • Then X is a random variable.
  • Which step in the procedure is left to chance?
  • What is the pdf of X?
example of a discrete pdf3
Example of a Discrete PDF
  • We may present the pdf as a table.
example of a discrete pdf4
Example of a Discrete PDF
  • Or we may present it as a stick graph.

P(X = x)

0.40

0.30

0.20

0.10

x

0

1

2

3

example of a discrete pdf5
Example of a Discrete PDF
  • Or we may present it as a histogram.

P(X = x)

0.40

0.30

0.20

0.10

x

0

1

2

3