Ootusväärtus

Ootusväärtus, in Estonian, translates to "expected value" in English. It is a fundamental concept in probability theory and statistics, representing the average outcome of a random variable if an experiment or process were repeated many times. Mathematically, the expected value of a discrete random variable X, denoted as E(X), is calculated by summing the product of each possible value of the variable and its corresponding probability. For a continuous random variable, it is found by integrating the product of the variable and its probability density function over its entire range.

The expected value is a weighted average, where the weights are the probabilities of each outcome. It is not necessarily a value that can actually occur, but rather a theoretical average. For instance, when rolling a fair six-sided die, the expected value is 3.5, even though a roll can only result in an integer from 1 to 6. This concept is widely used in decision-making under uncertainty, finance, game theory, and scientific research to assess the long-term average outcome of uncertain events or strategies. It provides a single numerical summary of the central tendency of a probability distribution.