# Appendix B - PowerPoint PPT Presentation

1 / 30

ECON 4550 Econometrics Memorial University of Newfoundland. Review of Probability Concepts. Appendix B. Adapted from Vera Tabakova’s notes . Appendix B: Review of Probability Concepts. B.1 Random Variables B.2 Probability Distributions

## Related searches for Appendix B

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Appendix B

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

ECON 4550

Econometrics

Memorial University of Newfoundland

Review of Probability Concepts

## Appendix B

### Appendix B: Review of Probability Concepts

• B.1 Random Variables

• B.2 Probability Distributions

• B.3 Joint, Marginal and Conditional Probability Distributions

• B.4 Properties of Probability Distributions

• B.5 Some Important Probability Distributions

• Principles of Econometrics, 3rd Edition

### B.1 Random Variables

• A random variable is a variable whose value is unknown until it is observed.

• A discrete random variable can take only a limited, or countable, number of values.

• A continuous random variable can take any value on an interval.

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

• The probability of an event is its “limiting relative frequency,” or the proportion of time it occurs in the long-run.

• The probability density function (pdf) for a discrete random variable indicates the probability of each possible value occurring.

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

Figure B.1 College Employment Probabilities

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

• The cumulative distribution function (cdf) is an alternative way to represent probabilities. The cdf of the random variable X, denoted F(x),gives the probability that Xis less than or equal to a specific value x

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

• For example, a binomial random variableX is the number of successes in n independent trials of identical experiments with probability of success p.

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-10

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-11

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

First: for winning only once in three weeks, likelihood is 0.189, see?

Times

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-12

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks…

The likelihood of winning exactly 2 games, no more or less:

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-13

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

So 3 times 0.147 = 0.441 is the likelihood of winning exactly 2 games

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-14

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

And 0.343 is the likelihood of winning exactly 3 games

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-15

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

For winning only once in three weeks: likelihood is 0.189

0.441 is the likelihood of winning exactly 2 games

0.343 is the likelihood of winning exactly 3 games

So 0.784 is how likely they are to win at least 2 games in the next 3 weeks

In STATA di Binomial(3,2,0.7) di Binomial(n,k,p)

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-16

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

So 0.784 is how likely they are to win at least 2 games in the next 3 weeks

In STATA di binomial(3,2,0.7) di Binomial(n,k,p) is the likelihood of winning 1 or less (See help binomial() and more generally help scalar and the click on define)

So we were looking for 1- binomial(3,2,0.7)

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-17

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

So 0.784 is how likely they are to win at least 2 games in the next 3 weeks

In SHAZAM, although there are similar commands, but it is a bit more cumbersome

See for example: http://shazam.econ.ubc.ca/intro/stat3.htm

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

Slide B-18

For example, if we know that the MUN basketball team has a chance of winning of 70% (p=0.7) and we want to know how likely they are to win at least 2 games in the next 3 weeks

http://www.zweigmedia.com/ThirdEdSite/stats/bernoulli.html

GRETL: Tools/p-value finder/binomial

### B.2 Probability Distributions

Figure B.2 PDF of a continuous random variable

If we have a continuous

Principles of Econometrics, 3rd Edition

### B.2 Probability Distributions

Principles of Econometrics, 3rd Edition

### B.3 Joint, Marginal and Conditional Probability Distributions

Principles of Econometrics, 3rd Edition

### B.3 Joint, Marginal and Conditional Probability Distributions

Principles of Econometrics, 3rd Edition

### B.3.1 Marginal Distributions

Principles of Econometrics, 3rd Edition

### B.3.1 Marginal Distributions

Principles of Econometrics, 3rd Edition

### B.3.2 Conditional Probability

Principles of Econometrics, 3rd Edition

### B.3.2 Conditional Probability

• Two random variables are statisticallyindependent if the conditional probability that Y = y given that X = x, is the same as the unconditional probability that Y = y.

Principles of Econometrics, 3rd Edition

### B.3.3 A Simple Experiment

Y = 1 if shaded Y = 0 if clear

X = numerical value (1, 2, 3, or 4)

Principles of Econometrics, 3rd Edition

### B.3.3 A Simple Experiment

Principles of Econometrics, 3rd Edition

### B.3.3 A Simple Experiment

Principles of Econometrics, 3rd Edition

### B.3.3 A Simple Experiment

Principles of Econometrics, 3rd Edition