Yhtenäisjakauma

Yhtenäisjakauma is the Finnish term for a uniform distribution, a probability distribution where all outcomes within a given range are equally likely. There are two main types: the discrete uniform distribution and the continuous uniform distribution.

In a discrete uniform distribution, the random variable can take on a finite number of values, each with the same probability. For example, if a fair six-sided die is rolled, the outcome can be any integer from 1 to 6, and each outcome has a probability of 1/6. The probability mass function (PMF) for a discrete uniform distribution over the set {a, a+1, ..., b} is P(X=k) = 1/(b-a+1) for k in {a, a+1, ..., b}, and 0 otherwise.

In a continuous uniform distribution, the random variable can take on any value within a given interval, say [a, b]. Every subinterval of the same length within [a, b] has the same probability of containing the random variable. The probability density function (PDF) for a continuous uniform distribution over the interval [a, b] is f(x) = 1/(b-a) for a <= x <= b, and 0 otherwise. The cumulative distribution function (CDF) is F(x) = 0 for x < a, F(x) = (x-a)/(b-a) for a <= x <= b, and F(x) = 1 for x > b.

The uniform distribution is fundamental in probability theory and statistics. It is often used as a baseline or a starting point for understanding more complex distributions. It also appears in contexts like random number generation, where algorithms aim to produce sequences of numbers that are uniformly distributed.