ootusteväärtuse

Ootusteväärtus, often translated as expected value, is a fundamental concept in probability theory and statistics. It represents the average outcome of a random phenomenon if the experiment or process were repeated many times. In simpler terms, it's the weighted average of all possible values that a random variable can take, where the weights are the probabilities of those values occurring.

For a discrete random variable X that can take values x₁, x₂, ..., xₙ with 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 calculated using an integral.

The expected value is a theoretical concept and does not necessarily represent a value that will actually occur in a single trial. However, it is crucial for understanding the long-run behavior of random processes. It plays a significant role in decision-making under uncertainty, risk assessment, and the development of statistical models. For instance, in games of chance, the expected value can indicate whether a game is favorable or unfavorable to the player in the long run.