Zufallsgröße

Zufallsgröße is the German term for a random variable. It is a variable whose value is a numerical outcome of a random phenomenon. In simpler terms, it's a quantity that can take on different values with a certain probability.

The concept of a Zufallsgröße is fundamental in probability theory and statistics. It allows us to mathematically describe and analyze random events. For example, the outcome of rolling a die can be represented by a Zufallsgröße, where the possible values are the integers from 1 to 6, each with a probability of 1/6.

Zufallsgrößen can be discrete or continuous. A discrete Zufallsgröße can only take on a finite number of values or a countably infinite number of values, such as the number of heads in a series of coin flips. A continuous Zufallsgröße can take on any value within a given range, like the height of a person or the temperature on a given day.

The behavior of a Zufallsgröße is described by its probability distribution. This distribution specifies the probability of each possible outcome. For discrete Zufallsgrößen, this is often given by a probability mass function, while for continuous Zufallsgrößen, it is given by a probability density function. Understanding the distribution of a Zufallsgröße is crucial for making predictions and drawing conclusions from data.