Ch2: Probability Theory

Some basics Definition of Probability Characteristics of Probability Distributions Descriptive statistics

1. Some Basics

A random experiment Population and Sample point An event Mutually exclusive and equally likely Random variable: r.v. for short An example: coin tossing

2. Definition of Probability

The classical definition

The empirical definition

Absolute frequency vs. relative frequency

( )

the number of outcomes favourable to A

the total number of outcomes

mP A

n

2. Definition of Probability (continued)

Probability distribution function (PDF) Joint probability Unconditional probability vs. conditional

probability Statistical independence

Independence vs. non-correlation( , ) ( ) ( )f X Y f X f Y

3. Characteristics of Probability Distributions

Moments

Population moments

Sample moments

Population Moments

(Population) mean (Expected value) (Population) variance & standard deviation (Population) covariance (Population) correlation coefficient (Population) skewness (population) kurtosis

Sample Moments

Sample mean Sample variance and sample standard deviation Sample covariance Sample correlation coefficient Sample skewness Sample kurtosis

4. Descriptive Statistics

Types of data Presentation of data Exploring data with graphical methods Exploring data with descriptive statistics Descriptive statistics Measures of location/central tendency Measures of dispersion Measures of shape Measures of association