1. Ch2: Probability Theory Some basics Definition of Probability Characteristics of Probability Distributions Descriptive statistics

2. 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

3. 2. Definition of Probability The classical definition The empirical definition Absolute frequency vs. relative frequency

4. 2. Definition of Probability (continued) Probability distribution function (PDF) Joint probability Unconditional probability vs. conditional probability Statistical independence Independence vs. non-correlation

5. 3. Characteristics of Probability Distributions Moments Population moments Sample moments

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

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

8. 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