todennäköisyysmassaa

todennäköisyysmassaa is a Finnish term that translates to probability mass in English. It is a fundamental concept in probability theory and statistics, particularly concerning discrete random variables. A probability mass function (PMF) assigns a probability to each possible value that a discrete random variable can take. This means that for a discrete random variable X, the probability mass function P(X=x) gives the probability that X is exactly equal to some value x.

The key properties of a probability mass function are that the probability for any specific value must be between 0 and 1, inclusive (0 <= P(X=x) <= 1). Furthermore, the sum of probabilities for all possible values of the random variable must equal 1. This is often expressed as the sum over all x of P(X=x) = 1. For example, if we consider the random variable representing the outcome of a fair six-sided die roll, the probability mass function would assign a probability of 1/6 to each of the values 1, 2, 3, 4, 5, and 6. The sum of these probabilities (6 * 1/6) equals 1, and each individual probability is between 0 and 1. The concept of probability mass is distinct from probability density, which is used for continuous random variables.