Tõenäosusmassi

Tõenäosusmassi is a Finnish term that translates to "probability mass" in English. It is a fundamental concept in probability theory, specifically when dealing with discrete random variables. A discrete random variable is one that can only take on a finite number of values or a countably infinite number of values.

The probability mass function (PMF) assigns a probability to each possible value that a discrete random variable can take. For a discrete random variable X, the probability mass function is denoted by P(X=x) or p(x), and it represents the probability that X is exactly equal to a specific value x. The sum of all probabilities in the probability mass function must equal 1. This means that the random variable is certain to take on one of its possible values.

For example, if X represents the outcome of a fair six-sided die roll, its possible values are {1, 2, 3, 4, 5, 6}. The probability mass function would assign a probability of 1/6 to each of these values, as each outcome is equally likely. The sum of these probabilities (6 * 1/6) equals 1.

The concept of probability mass is crucial for understanding the behavior and distribution of discrete random variables, forming the basis for many statistical calculations and models.