todennäköisyysmassalla

todennäköisyysmassalla is a Finnish term that translates to "probability mass" in English. It refers to the probability that a discrete random variable takes on a specific value. In simpler terms, it's the chance of a particular outcome occurring when you have a limited, countable number of possible outcomes.

This concept is fundamental in probability theory and statistics, particularly when dealing with discrete probability distributions. A discrete random variable can only take on a finite number of values or a countably infinite number of values. For each possible value that the variable can assume, there is an associated probability mass. The sum of all these probability masses for all possible values of the random variable must equal 1, meaning that the probability of one of the possible outcomes occurring is certain.

For example, if you roll a fair six-sided die, the random variable is the number that appears on the top face. The possible values are 1, 2, 3, 4, 5, and 6. Since the die is fair, the probability mass for each of these values is 1/6. The sum of these probabilities (1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6) equals 1. In contrast, continuous random variables use probability density functions, not probability masses, because the probability of a continuous variable taking on any exact single value is infinitesimally small.