Download Sec 5.1 Probability Distributions

Bluman, Chapter 5
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In how many ways can the
letters in the following words be
arranged?
1)
2)
3)
4)
Fancy
Algebra
Mississippi
Hannah
Bluman, Chapter 5
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A family has four children.

•
•
•
•
•
Let x be the number of boys in the family
find:
𝑃(0)
𝑃(1)
𝑃(2)
𝑃(3)
𝑃(4)
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Bluman, Chapter 5
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Chapter 5
Discrete Probability
Distributions
McGraw-Hill, Bluman, 7th ed, 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
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.
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
Bluman, Chapter 5
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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
Bluman, Chapter 5
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Example 5-2: Tossing Coins
Display the probability distribution for tossing
three coins. If x is the number of heads.
.
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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.
𝑝 𝑥 =1
0 ≤ 𝑝(𝑥) ≤ 1
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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
On your Own
 Read
Example
5-4 page 257


Applying Concepts
page 257
Exercises 5-1 page
258 # 1-18 all, 23
and 27.
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