Verwachtingwaarde

Verwachtingwaarde, also known as expected value, is a fundamental concept in probability theory and statistics. It represents the average value of a random variable over a large number of trials. In other words, it is the long-term average outcome of a random event.

The verwachtingwaarde of a discrete random variable X, which can take on a finite or countably infinite number of values, is calculated by multiplying each possible value of X by its probability and then summing these products. Mathematically, this is expressed as:

E(X) = Σ [x_i * P(X = x_i)]

where E(X) denotes the verwachtingwaarde of X, x_i are the possible values of X, and P(X = x_i) is the probability of X taking the value x_i.

For a continuous random variable, the verwachtingwaarde is calculated using an integral rather than a sum. This is expressed as:

E(X) = ∫ [x * f(x) dx]

where f(x) is the probability density function of X.

The verwachtingwaarde is a crucial concept in decision theory, as it helps in making informed decisions under uncertainty. It is also used in various fields such as finance, insurance, and engineering to model and analyze random phenomena.