Probability and Probability Distributions - An Introduction

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En provenance du cours de University of London

Statistics for International Business

94 notes

University of London

Statistics for International Business

94 notes

Cours 4 sur 6 dans Specialization International Business Essentials

This course introduces core areas of statistics that will be useful in business and for several MBA modules. It covers a variety of ways to present data, probability, and statistical estimation. You can test your understanding as you progress, while more advanced content is available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit www.londoninternational.ac.uk/mba This course is endorsed by CMI

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Probability and Probability Distributions

Probability theory is a young arrival in mathematics- and probability applied to practice is almost non-existent as a discipline. We should all understand probability, and this lecture will help you to do that. It’s important for you to understand first that the world in which your future occurs is not deterministic- and there are future outcomes where a probability model cannot be developed… This week, we will cover the basic definition of probability, the rules of probability,random variables, -probability density functions, expectations of a random variable and Bivariate random variables.

Probability and Probability Distributions - An Introduction4:31

1. Introduction1:13

2. Random Experiment2:14

4: Probability1:31

4.1: The Definition of Probability3:42

4.2: Probability Rules1:53

4.3: The Addition Rule of Probabilities2:10

4.4: Conditional Probability2:03

4.5: The Multiplication Rule of Probabilities0:49

5: Random Variables2:28

5.1: The Probability Distribution Function2:12

6: Properties of Discrete Random Variables1:28

6.1: The Variance of a Discrete Random Variable1:58

7. Continuous Random Variables3:01

8. The Probability Density Function1:39

9. The Expectations for Continuous Random Variables3:17

Probability and Probability Distributions - Summary2:28

Rencontrer les enseignants

George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

Well, hello everybody, and welcome to the third lecture of the Statistics for

International Business MOOC.

This week we will introduce to you the concept of probability and distributions.

The material presented this week shows why we all should understand probability.

As a financial trader and professor, Nassim Nicholas Taleb points out,

probability is about luck disguised and perceived as skills, and more generally,

randomness, disguised and perceived as non-randomness, that is determinism.

More generally,

we underestimate the share of randomness in about everything around us.

Probability is a young arrival in mathematics.

And probability applied to practice is almost nonexistent as a discipline.

We seem to have evidence that what is called carriage

comes from an underestimation of the share of randomness in things,

rather than the more noble ability to stick one's neck out for a given belief.

So this week we will focus understanding probability.

This will allow us to be prepared and

avoid some of the effects of what I mentioned earlier.

However, we will also discuss why it is important to understand

that not everything can be predicted.

For example, natural disasters or

sudden political events, may have a huge impact to business and economics.

These unpredictable events have been called black swans.

We begin our presentation of probability

to represent events with uncertain outcomes.

We begin to adopt these ideas, and thereby developed probability models.

We begin with discrete random variables.

And then we will present probability models that are adequate and

appropriate for continuous random variables.

Probability models are extensively adopted to solve a number of business problems.

Many of these applications are developed during the week.

Suppose, for example, that you own a business renting a variety of equipment.

From past experience, you know that 45% of the buyers

entering your store want to rent a certain type of device.

You have three such devices available at the moment.

Six unrelated people enter the store.

And we note that the likelihood that one rents a particular device is independent

of the probability that others will ask to rent the same kind of device.

So we ask ourselves, what is the probability that these six people who

have entered our store are seeking to rent a total of four or five devices?

Now if that happens, we will have missed some profit opportunities.

And of course our customers will not be happy.

The probability of the events that is the number of devices that are desired

by the clients, may be computed using a kind of model called the binomial model.

The problem we've just presented is just an example of a situation where

a probability may be computed using a standard probability model.

These models simplify problem-solving and the calculation of probabilities.

However, when we want to use such a standard model,

some important assumptions must be satisfied.

So we begin with some definitions.

And then we move on to present several important models

that are used extensively in business, financial, and economic applications.

Finally, we generalize values of these concepts related to probability

to continuous random variables.

And we conclude by discussing probability distributions.

Thank you.

[MUSIC]

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