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