Chap05 Discrete Probability Distribution

Business Statistics
Chapter 5
Some Important Discrete
Probability Distributions

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Chapter Goals
After completing this chapter, you should be able to:  Interpret the mean and standard deviation for a discrete probability distribution
 Explain covariance and its application in finance
 Use the binomial probability distribution to find probabilities  Describe when to apply the binomial distribution
 Use Poisson discrete probability distributions to find probabilities
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Definitions
Random Variables
 A random variable represents a possible numerical value from an uncertain event.
 Discrete random variables produce outcomes that come from a counting process (e.g. number of courses you are taking this semester).
 Continuous random variables produce outcomes that come from a measurement (e.g. your annual salary, or your weight).
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Definitions
Random Variables
Random
Variables
Ch. 5

Discrete
Random Variable

Continuous
Random Variable

Ch. 6

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Discrete Random Variables
 Can only assume a countable number of values
Examples:
 Roll a die twice
Let X be the number of times 4 comes up
(then X could be 0, 1, or 2 times)

 Toss a coin 5 times.
Let X be the number of heads
(then X = 0, 1, 2, 3, 4, or 5)
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Probability Distribution for a
Discrete Random Variable
 A probability distribution (or probability mass function )(pdf) for a discrete random variable is a mutually exclusive listing of all possible numerical outcomes for that random variable such that a particular probability of occurrence is associated with each outcome.
Number of Classes
Taken

Probability

2

0.2

3

0.4

4

0.24

5

0.16
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Discrete Probability Distribution
Experiment: Toss 2 Coins.

T
T
H
H

T
H
T
H

Probability Distribution
X Value

Probability

0

1/4 = .25

1

2/4 = .50

2

1/4 = .25

Probability

4 possible outcomes

Let X = # heads.

.50
.25

0

1

2

X
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Discrete Random Variable
Summary Measures
 Expected Value (or mean) of a discrete distribution (Weighted