forventningsværdierne

Forventningsværdierne, a Danish term, translates to expected values in English. In probability theory and statistics, the expected value of a random variable is a fundamental concept representing the long-run average value of that variable. It is calculated by multiplying each possible outcome of the random variable by its probability and then summing these products.

The expected value is not necessarily one of the possible outcomes of the random variable. Instead, it serves as a weighted average, where the weights are the probabilities of each outcome. For a discrete random variable X with possible values x₁, x₂, ..., xn and corresponding probabilities P(X=x₁), P(X=x₂), ..., P(X=xn), the expected value E(X) is given by the formula E(X) = Σ [xi * P(X=xi)]. For a continuous random variable, the sum is replaced by an integral.

The concept of expected value is widely used in various fields. In finance, it helps in assessing the potential return on investment. In decision theory, it aids in choosing between different options by comparing their expected outcomes. In gambling, it can be used to determine the fairness of a game. Understanding forventningsværdierne is crucial for making informed decisions when dealing with uncertainty and probabilistic events.