Bluman, Chapter 5 1

Bluman, Chapter 5 2

In how many ways can the

letters in the following words be

arranged?

1) Fancy

2) Algebra

3) Mississippi

4) Hannah

Bluman, Chapter 5 3

Chapter 5

Discrete Probability Distributions

McGraw-Hill, Bluman, 7th ed, Chapter 5 4

Chapter 5 Overview

Introduction

5-1 Probability Distributions

5-2 Mean, Variance, Standard Deviation,

and Expectation

5-3 The Binomial Distribution

5-4 Other Types of Distributions

Bluman, Chapter 5 5

Chapter 5 Objectives 1. Construct a probability distribution for a random

variable.

2. Find the mean, variance, standard deviation, and

expected value for a discrete random variable.

3. Find the exact probability for X successes in n trials of

a binomial experiment.

4. Find the mean, variance, and standard deviation for

the variable of a binomial distribution.

5. Find probabilities for outcomes of variables, using the

Poisson, hypergeometric, and multinomial

distributions.

Bluman, Chapter 5 6

Variables

Discrete variables have a finite number of possible values or an infinite number of values that can be counted.

Result of a count.

Continuous variables are variables that can assume all values in the interval between any two given values.

Result of a measurement.

Sec 5.1

Probability Distribution

Bluman, Chapter 5 8

5.1 Probability Distributions

A random variable is a variable whose values

are determined by chance.

A discrete probability distribution consists of

the values a random variable can assume and

the corresponding probabilities of the values.

The sum of the probabilities of all events in a

sample space add up to 1. Each probability is

between 0 and 1, inclusively.

Bluman, Chapter 5 9

Chapter 5

Discrete Probability Distributions

Section 5-1

Example 5-1

Page #254

Bluman, Chapter 5 10

Example 5-1: Rolling a Die

Construct a probability distribution for rolling a

single die.

Bluman, Chapter 5 11

Chapter 5

Discrete Probability Distributions

Section 5-1

Example 5-2

Page #254

Bluman, Chapter 5 12

Example 5-2: Tossing Coins

Display the probability distribution for tossing

three coins. If x is the number of heads.

.

Bluman, Chapter 5 13

Example 5-2: Tossing Coins

Represent graphically the probability distribution

for the sample space for tossing three coins.

.

Bluman, Chapter 5 14

Requirements for Prob Dist.

𝑝 𝑥 = 1

0 ≤ 𝑝(𝑥) ≤ 1

Bluman, Chapter 5 15

Example 5-3

During the summer months, a rental agency keeps track of the number of chain saws it rents each day during a period of 90 days. The number of saws rented per day is represented by the variable x. The results are shown here. Compute the probability P(x) for each x, and construct a probability distribution and graph for the data.

x Number of Days

0 45

1 30

2 15

Total 90

5-2 Mean, Variance, Standard

Deviation, and Expectation

MEAN: X P X

2 2 2

VARIANCE:

X P X

Bluman, Chapter 5 17

On your Own

Read Example

5-4 page 257

Applying Concepts

page 257

Exercises 5-1 page

258 # 1-18 all, 23

and 27.

Bluman, Chapter 5 18