gleichwahrscheinlichkeitsmaß

Gleichwahrscheinlichkeitsmaß, also known as the uniform probability measure, is a fundamental concept in probability theory. It describes a situation where every possible outcome of a random experiment has an equal chance of occurring. This means that for a finite sample space, if there are 'n' possible outcomes, each outcome has a probability of 1/n.

The concept is widely used in introductory probability examples, such as rolling a fair die or flipping a fair coin. In these scenarios, each face of the die or side of the coin has an equal probability of appearing. Similarly, when drawing a card from a well-shuffled deck, each card has an equal likelihood of being selected.

In the context of continuous probability, a gleichwahrscheinlichkeitsmaß is represented by a uniform distribution. For instance, a random variable uniformly distributed over an interval [a, b] assigns equal probability density to all values within that interval. The probability density function (PDF) for a continuous uniform distribution over [a, b] is 1/(b-a) for values within the interval and 0 otherwise. This ensures that the total probability over the interval equals 1. The gleichwahrscheinlichkeitsmaß simplifies many probability calculations and serves as a baseline for understanding more complex probability distributions.