Part I: Probability

Random Experiments and Probability

• Random Experiments

• Sample Space

• Probabilities

• Axiomatic Definition of Probability
• Laplace Experiments
• Basic Rules of Probability and Combinatorics

• Conditional Probability

• Conditional Probability
• Total Probability and Bayes`Theorem
• Independence of Events

Random Variables and Distributions

• Random Variables

• Cumulative Distribution Function
• Quantile Function
• Discrete Random Variables
• Continuous Random Variables
• Affine-Linear Transformation of Random Variables

• Distribution Parameter

• Expected Value
• Variance
• Tchebychev Inequality
• Skewness

• Special Discrete Distributions

• Binomial Distribution
• Poisson Distribution
• Geometric Distribution
• Hypergeometric Distribution
• Approximation of Discrete Distributions

• Special Continuous Distributions

• Rectangular Distribution
• Exponential Distribution
• Normal Distribution

Multivariate Distributions and Limit Theorems

• Joint Distribution of Random Variables

• Joint and Conditional Distribution of Random Variables
• Covariance and Coefficient of Correlation
• Sums of Random Variables

• Limit Theorems

• Weak Law of Large Numbers
• Central Limit Theorem

Part II: Statistical Inference

Samples and Sample Functions

• Random Sampling
• Statistics (Functions of Random Samples)
• Statisticas for Normally Distributed Samples
• t-Distribution

Method of Estimation for Parameters

• Estimation of Parameters

• Point Estimation
• Unbiasedness and Consistency
• Maximum-Likelihood-Estimator
• Estimation of Expected Values
• Estimation of Probabilities
• Estimation of Variances and Standard Deviations

• Interval Estimation of Expected Values and Probabilities

• Confidence Intervals of Expected Values
• Confidence Intervals of Probabilities
• Sample Size

Testing Procedure

• Estimation of Parameters

• Testing Problem, Hypotheses
• Sampling Errors (Type 1 & 2)
• p-Value

• Testing of Expected Values

• One Sample Tests for Expected Values and Probabilities
• Two Sample Tests for Expected Values and Probabilities

• Tests for Probabilites

• Tests for one Probability or Fractile
• Comparison of two Probabilites or Fractiles

Linear Regression

• Simple Linear Regression

• Simple Linear Regression Model
• Point Estimation of Coefficients
• Interval Estimation of the Parameters
• Tests for the Parameters

• Multiple Linear Regression

• Interpretation of the Parameters
• Tests for the Parameter