Sannolikhetsförväntan

Sannolikhetsförväntan, often referred to as "förväntningsvärde" or simply "väntan" in Swedish, is a fundamental concept in probability theory and statistics. It represents the average value of a random variable over a large number of trials. Mathematically, 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 calculated as the sum of each possible value multiplied by its probability: E(X) = Σ [xᵢ * P(X=xᵢ)]. For a continuous random variable, the expected value is found by integrating the product of the variable's value and its probability density function over its range.

The expected value is not necessarily one of the possible outcomes of the random variable. Instead, it's a weighted average that indicates where the distribution of outcomes is centered. It has important applications in various fields, including finance, where it's used to estimate the potential return on investments, and in decision theory, to evaluate the average outcome of different choices. Understanding sannolikhetsförväntan is crucial for analyzing random phenomena and making informed predictions.