Chapter 7 Lesson 7.2 Random Variables and Probability Distributions 7.2 Probability Distributions...

Chapter 7Lesson 7.2

Random Variables and Probability Distributions7.2 Probability Distributions for

Discrete Random Variables

Probability Distributions for Discrete Random Variables

Probability distribution is a model that describes the long-run

behavior of a variable.

Number of Pets

Prob

abilit

y

In a Wolf City (a fictional place), regulations prohibit no more than five dogs or cats per household. Let x = the number of dogs and cats in a randomly selected household in Wolf City

x 0 1 2 3 4 5P(x) .26 .31 .21 .13 .06 .03

Is this variable discrete or continuous?What are the possible values for x?

The Department of Animal Control has collected data over the course of

several years. They have estimated the long-run probabilities for the

values of x.

What do you notice about the sum of these probabilities?

This is called a discrete probability distribution. It can also be

displayed in a histogram with the probability on the vertical axis.

Discrete Probability Distribution

1) Gives the probabilities associated with each possible x value

2) Each probability is the long-run relative frequency of occurrence of the corresponding x-value when the chance experiment is performed a very large number of times

3) Usually displayed in a table, but can be displayed with a histogram or formula

Dogs and Cats Revisited . . . Let x = the number of dogs or cats per household in Wolf City

x 0 1 2 3 4 5P(x) .26 .31 .21 .13 .06 .03

What is the probability that a randomly selected household in Wolf City has at most 2 pets?

What does this mean?

P(x < 2) =

Just add the probabilities for 0, 1, and 2

.26 + .31 + .21 = .78

Dogs and Cats Revisited . . . Let x = the number of dogs or cats per household in Wolf City

x 0 1 2 3 4 5P(x) .26 .31 .21 .13 .06 .03

What is the probability that a randomly selected household in Wolf City has less than 2 pets?

What does this mean?

P(x < 2) =

Notice that this probability does NOT include 2!

.26 + .31 = .57

Dogs and Cats Revisited . . . Let x = the number of dogs or cats per household in Wolf City

x 0 1 2 3 4 5P(x) .26 .31 .21 .13 .06 .03

What is the probability that a randomly selected household in Wolf City has more than 1 but no more than 4 pets?

What does this mean?

P(1 < x < 4) =

.21 + .13 + .06 = .40

When calculating probabilities for discrete random variables, you MUST pay close attention to whether certain values are

included (< or >) or not included (< or >) in the calculation.

Homework

• Pg.408: #7.8, 9, 11, 12