Upload
henry-hardy
View
215
Download
0
Embed Size (px)
Citation preview
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