Bernoulli distribution

The random variable X takes only the values 0 or 1 (has a support T = {0, 1})

Examples: coin toss

Discrete uniform distribution

All possible values have the same probability

Examples: thrown number when throwing a dice once

Continuous uniform distribution

Binomial distribution (\(B(n, \pi)\))

For n independent repetitions of a Bernoulli experiment

Example: n independent draws of lottery with two possible outcomes prize or blank

Poisson distribution (\(Po(\lambda)\))

Count the number of (random) incidents / events within a fixed time interval, if they can occur at any time

Examples: Property insurance claims within one year; Number of cases of a rare disease in one month

Exponential distribution

Results from the modeling of durations where time is measured - at least approximately - continuously

Examples: : Lifetime of a product or technical system

Normal distribution/ Gaussian distribution\(N(\mu, o^2)\)

The distribution function of the (standardized) sum of n independent, identically distributed random variables

Examples: Deviations from target values in the production of equipment, physical sizes (height, weight)

\(\chi ^2\) distribution (\(\chi ^2(n)\)

Distribution of the sum of independent squared standard normally distributed random variables

t distribution (t(n))

Required especially for parameter tests and confidence intervals for parameters in statistical inference

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