Pistetodennäköisyysfunktiota

Pistetodennäköisyys, in statistics and probability theory, refers to the probability that a continuous random variable will take on a specific value. For continuous probability distributions, the probability of any single point occurring is zero. This is because there are infinitely many possible values a continuous variable can take. Instead of assigning probability to individual points, probability is assigned to intervals. The probability density function (PDF), denoted by f(x), describes the relative likelihood for a continuous random variable to take on a given value. The area under the PDF curve between two points represents the probability that the variable falls within that interval. Therefore, the integral of the PDF from a to b, ∫[a, b] f(x) dx, gives the probability P(a ≤ X ≤ b). For any specific value 'c', the probability P(X = c) is the integral from c to c, which is always zero. This concept distinguishes continuous variables from discrete variables, where individual outcomes can have non-zero probabilities. The term pistetodennäköisyys is a Finnish term that translates directly to "point probability."