Chebyshevetyisyyksiä
Chebyshevetyisyyksiä is a Finnish term that translates to "Chebyshev's inequalities" in English. These are a set of mathematical inequalities that provide an upper bound on the probability that a random variable will deviate from its mean by more than a certain amount. The most well-known and general form of Chebyshev's inequality states that for any random variable X with finite expected value (mean) denoted by $\mu$ and finite non-zero variance denoted by $\sigma^2$, and for any positive real number $k$, the probability that X is more than $k$ standard deviations away from its mean is at most $1/k^2$. Mathematically, this is expressed as $P(|X - \mu| \ge k\sigma) \le 1/k^2$.
Chebyshev's inequalities are powerful because they hold for any probability distribution, regardless of its specific shape.