ootusteväärtus

Ootusteväärtus refers to the expected value of a random variable. It is a fundamental concept in probability theory and statistics, representing the average outcome of a random event if it were repeated many times. Mathematically, for a discrete random variable X with possible values x_1, x_2, ..., x_n and corresponding probabilities P(X=x_i), the expected value E[X] is calculated as the sum of each possible value multiplied by its probability: E[X] = Σ x_i * P(X=x_i). For a continuous random variable, the expected value is found by integrating the product of the variable and its probability density function over its entire range.

The expected value is not necessarily a value that the random variable can actually take. Instead, it's a weighted average that reflects the central tendency of the distribution. It plays a crucial role in decision-making under uncertainty, risk assessment, and statistical inference. For example, in finance, the expected return on an investment is a key metric for evaluating its potential profitability. In games of chance, the expected value of a bet can determine whether the game is favorable or unfavorable to the player in the long run. Understanding ootusteväärtus allows for a quantitative analysis of probabilistic outcomes.