20160404 
 Why probability and inferential statistics?
 Random experiment and probability space
 Set of (all possible) outcomes
 Set of (all possible) events, σalgebra
 Probability measure

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Probability and Conditional Expectation
 Steyer, R., & Eid, M. (2013). Messen und Testen. Berlin: Springer. (Anhänge: Mathematische Grundbegriffe, Mengen und Mengenoperationen, Relationen und Relative, Abbildungen und Homomorphismen)
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20160411 
 Rules of computation for probabilities
 Example: Joe and Ann, some events and their probabilities
 Conditional probability
 Multiplication rule

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Slides (updated 20160415)
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20160418 
 Theorem of Total Probability and Bayes Theorem
 Independence of events
 Independence of sets of events
 Conditionalprobability measure
 First ideas about random variables
 Image and inverse image of a set under a mapping
 Events represented by a random variable

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Slides
Blackboard sketches

20160425 
 Random variable
 Sigmaalgebra generated by a random variable
 Sigmaalgebra generated by a set system
 Borel sigmaalgebra
 Realvalued random variable
 Numerical random variable
 Independence of two random variables

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20160502 
 Independence of n random variables
 JoeAnn example with selfselection
 Distribution of a random variable
 The distribution as a new probability measure
 Distribution function of a realvalued random variable
 Discrete random variable and its probability function
 Example: Indicator variable and its distribution
 Example: binomial distribution

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Slides (updated 20160512)
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20160509 
 Continuous random variable and its density
 Density of the normal distribution
 Expectation of a discrete random variable
 Expectation: General definition
 Expectation and mean squared error
 Transformation Theorem
 Variance and standard deviation
 Covariance and correlation
 Independence and covariance
 Rules of computation for expectations
 Expectation of a binomially distributed random variable

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Slides (updated 20160524)
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20160523 
 Implications of independence on covariance and correlation
 Rules of computation for expectations
 Example: Expectation of a binomially distributed random variable
 Rules of computation for variances
 Example: Variance of an indicator variable
 Example: Variance of a binomially distributed random variable
 Rules of computation for covariances
 Linear quasiregression
 Conditional expectation value

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20160530 
 Definition of a sample
 Estimator (a random variable) and estimate (its value)
 Expectation of a sample mean
 Expectation of a sample variance
 Variance of a sample mean
 Standard (deviation) error of a sample mean
 Unbiased estimator of the variance
 An estimator of the standard error of a sample mean

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20160606 
 Standard error of the sample mean: Example using the binomial distribution
 Summary of the most important concept concerning sample and estimator
 Examples for hypotheses in significance tests
 Test statistic in significance tests
 Basic idea of a significance test
 Example of a onesided significance test
 Null hypothesis and alternative hypothesis
 Example of a twosided significance test
 Area of rejection and area of nonrejection

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Slides (updated 20160614)
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20160613 
 Error of type I and II in significance testing
 Error probabilities alpha and beta
 Power of a test
 How to decrease these error probabilities
 Illustrating alpha and betaerror probabilities by a normally distributed test statistic
 Density of the normal distribution
 RPrograms related to the normal distribution

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Slides
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20160620 
 Density of the chisquare distribution and Rprograms
 Density of the tdistribution and Rprograms
 Density of the Fdistribution and Rprograms

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20160627 
 Confidence interval
 Central limit theorem

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Slides
Materials
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20160704 

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