1Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Chapter 7 Random Variables

2Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

OverviewThis chapter will deal with the construction of

probability distributions

by combining the methods of Chapter 1 with the those of Chapter 6.

Probability Distributions will describe what will probably happen instead of what

actually did happen.

3Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Combining Descriptive Statistics Methods and Probabilities to Form a Theoretical Model of

Behavior

Chapter 6

Chapter 1 Chapter 7

4Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

§ 7.1

Random Variables

5Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Definitions Random Variable

a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure

Probability Distribution

a graph, table, or formula that gives the probability for each value of the random variable

6Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Probability DistributionNumber of Girls Among Fourteen Newborn Babies

0 1 2 3 4 5 6 7 8 91011121314

0.0000.0010.0060.0220.0610.1220.1830.2090.1830.1220.0610.0220.0060.0010.000

x P(x)

Table 4-1

7Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

DefinitionsDiscrete random variable

has either a finite number of values or countable number of values, where ‘countable’ refers to the fact that there might be infinitely many values, but they result from a counting process.

8Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Figure 4-3

Probability Histogram

9Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Example: JSL Appliances• Discrete random variable with a finite number of values

Let x = number of TV sets sold at the store in one day where x can take on 5 values (0, 1, 2, 3, 4)

• Discrete random variable with an infinite sequence of values

Let x = number of customers arriving in one day where x can take on the values 0, 1, 2, . . .

We can count the customers arriving, but there is no finite upper limit on the number that might arrive.

10Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

DefinitionsContinuous random variable

has infinitely many values, and those values can be associated with measurements on a continuous scale with no gaps or interruptions.

11Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Requirements for Probability Distribution

12Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Requirements for Probability Distribution

P(x) = 1 where x assumes all possible values

13Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Requirements for Probability Distribution

P(x) = 1 where x assumes all possible values

0 P(x) 1 for every value of x