oodatusarvu

Oodatusarvu, often translated as expected value, is a fundamental concept in probability theory and statistics. It represents the average outcome of a random event if that event were to be repeated many times. 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 value multiplied by its probability: E(X) = Σ [xi * P(X=xi)]. For a continuous random variable with probability density function f(x), the expected value is given by the integral E(X) = ∫ x * f(x) dx.

The expected value is not necessarily one of the possible outcomes of the random variable. Instead, it's a weighted average that summarizes the central tendency of a probability distribution. It is widely used in decision-making under uncertainty, finance, gambling, and game theory. For instance, in a game of chance, the expected value of a bet can help determine if it is favorable or unfavorable in the long run. In finance, it is used to estimate the potential return on an investment. The concept is also crucial in statistical inference for estimating population parameters.