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Chapter 5
Discrete Probability
Distributions
Bluman, Chapter 5
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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
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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.
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Variables
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Variables
Discrete variables have a finite number of
possible values or an infinite number of
values that can be counted.
Result of a count.
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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.
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Sec 5.1
Probability Distribution
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5.1 Probability Distributions

A random variable is a variable whose values
are determined by chance.
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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.
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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.
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Chapter 5
Discrete Probability Distributions
Section 5-1
Example 5-1
Page #254
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Example 5-1: Rolling a Die
Construct a probability distribution for rolling a
single die.
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Example 5-1: Rolling a Die
Construct a probability distribution for rolling a
single die.
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Chapter 5
Discrete Probability Distributions
Section 5-1
Example 5-2
Page #254
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Example 5-2: Tossing Coins
Represent graphically the probability distribution
for the sample space for tossing three coins.
.
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Example 5-2: Tossing Coins
Represent graphically the probability distribution
for the sample space for tossing three coins.
.
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Requirements for Prob Dist.

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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
1
2
45
30
15
Total 90
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5-2 Mean, Variance, Standard
Deviation, and Expectation
Bluman, Chapter 5
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5-2 Mean, Variance, Standard
Deviation, and Expectation
Bluman, Chapter 5
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5-2 Mean, Variance, Standard
Deviation, and Expectation
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On your Own
 Read
Example
5-4 page 257

Exercises 5-1 page
258 # 1-18 all, 23 and
27.
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