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Ch2: Probability Theory

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

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Ch2: Probability Theory

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  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

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