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Welcome to Chapter 5 MBA 541. B ENEDICTINE U NIVERSITY Probability - Distributions A Survey of Probability Concepts Chapter 5. Chapter 5. Please, Read Pages 139 – 146 in Chapter 5 in Lind before viewing this presentation. Only part of Chapter 5 will be covered. Statistical

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Welcome to Chapter 5 MBA 541

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Welcome to Chapter 5MBA 541

BENEDICTINEUNIVERSITY

• Probability - Distributions

• A Survey of Probability Concepts

• Chapter 5

Chapter 5

Read Pages 139 – 146 in Chapter 5 in Lind before viewing this presentation.

Only part of Chapter 5 will be covered.

Statistical

Techniques in

Economics

Lind

Goals

When you have completed this chapter, you will be able to:

• ONE

• Define Probability.

• TWO

• Describe the classical, empirical, and subjective approaches to probability.

• THREE

• Understand the terms: experiment, event, and outcome.

What is a Probability?

A Probability is a measure of the likelihood that an event in the future will happen.

Definitions of Probability

• There are three definitions of probability: classical, empirical, and subjective.

• The Classical definition applies when there are n equally likely outcomes.

• The Empiricaldefinition applies when the number of times the event happens is divided by the number of observations.

• Subjective probability is based on whatever information is available.

Definition of Experiment

An Experiment is the observation of some activity or the act of taking some measurements

Definitions of Outcome and Event

• An Outcome is the particular result of an experiment.

• An Event is the collection of one or more outcomes of an experiment.

• The following items illustrate these definitions:

• Experiment: A fair die is cast.

• Possible Outcomes: the numbers 1, 2, 3, 4, 5, 6

• One Possible Event: The occurrence of an even number. That is, the collection of the outcomes 2, 4, and 6.

Mutually Exclusive Events

• Events are Mutually Exclusive if the occurrence of any one event means that none of the others can occur at the same time.

• As an example of Mutually Exclusive:

• Rolling a 2 precludes rolling a 1, 3, 4, 5, 6 on the same roll.

Collectively Exhaustive Events

• Events are Collectively Exhaustive if at least one of the events must occur when an experiment is conducted.

• As an example of Collectively Exhaustive:

• Consider a die-tossing experiment.

• One possible event is rolling an even number.

• Another possible event is rolling an odd number.

• These two events are Collectively Exhaustive because every outcome of a die-toss will be either even or odd.

Classical Probability

• Classical Probability is based on the assumption that the outcomes of an experiment are equally likely.

• The value for the Classical Probability will always be between 0 and 1 inclusive and is given by the following formula:

Example 1

• This is an example of the classical definition of probability.

• What is the probability of drawing the Queen of Hearts from an honest deck of cards?

Empirical Probability

• With Empirical Probability, the probability of an event happening is determined by observing what fraction of the time similar events happened in the past.

• The value for the Empirical Probability will always be between 0 and 1 inclusive and is given by the following formula:

Example 2

• This is an example of the empirical definition of probability.

• Throughout her teaching career Professor Jones has awarded 186 A’s out of 1,200 students.

• What is the probability that a student in her section this semester will receive an A?

Subjective Probability

• Subjective Probability is used when there is little or no past experience or information on which to compute a probability.

• Examples of subjective probability are:

• Estimating the probability that the Washington Redskins will win the Super Bowl this year.

• Estimating the probability that mortgage rates for home loans will top 8 percent.

Summary of Approaches to Probability

Approaches to

Probability

Subjective

Objective

Classical

Probability

Empirical

Probability

Based on available information

Based on equally likely outcomes

Based on relative frequencies

Summary and Conclusions

• Introduced the language of probability.

• Outlined and introduced the concepts of probability.

• Probability theory helps to quantify the probability (or risk) of future events.

• Probability theory can help with decision making via risk analysis.