todennäköisyysmassasta

todennäköisyysmassasta is a Finnish term that translates to probability mass. It is a fundamental concept in probability theory and statistics, specifically when dealing with discrete random variables. A probability mass function (PMF) assigns a probability to each possible value that a discrete random variable can take. In simpler terms, it tells you how likely it is for a particular outcome to occur from a set of discrete possibilities.

For a random variable X, the probability mass function is denoted by P(X = x). This value represents the probability that the random variable X will take on the specific value x. The sum of all probabilities in a probability mass function must equal 1, meaning that the random variable is guaranteed to take on one of its possible values. The values that the random variable can take are typically countable, such as integers.

For example, consider the random variable representing the outcome of rolling a fair six-sided die. The possible values are 1, 2, 3, 4, 5, and 6. The probability mass function for this variable would assign a probability of 1/6 to each of these outcomes, as each face has an equal chance of appearing. If the die were biased, the probabilities for each outcome would be different, but their sum would still be 1. This concept is crucial for understanding discrete probability distributions like the Bernoulli, binomial, and Poisson distributions.