Lamun variabel random ''X'':Ω->'''R''' aya dina probabilityruang spaceprobabiliti (Ω, ''P'') diberekeun, urang bisa nanyakeun saperti kieu "HowSabaraha likelymungkin is it that the value ofnilai ''X'' isleuwih biggergede thantinimbang 2?". ThisIeu issarua thejeung samekamungkinan as the probability of the eventkajadian {''s'' indina Ω : ''X''(''s'') > 2} which is oftennu writtensalawasna asditulis P(''X'' > 2) forkeur shortnyingketna.
RecordingRekaman allsakabeh theserentang probabilitieshasil ofieu outputkamungkinan rangestina ofnilai-real a real-valuedvariabel random variable ''X'' yields thengahasilkeun [[probability distribution]] of ''X''. TheSebaran probability distributionkamungkinan "forgetspoho" aboutngeunaan thebagean particularruang probabilityprobabiliti spacedipake usedkeur to definengartikeun ''X'' andjeung onlyngan recordsdirekam thedina probabilitiesvariasi of various values ofnilai ''X''. Such a probability distribution canSaperti alwayssebaran bekamngkinan capturedsalawasna bykawengku itsdina [[cumulative distribution function]]
:<math>F_X(x) = \operatorname{P}(X < x)</math>
andsarta sometimeskadangkala alsomake using aoge [[probability density function]]. InDina watesan [[measure theory|measure-theoretic]] terms, wedipake use thevariabel random variable ''X'' tokeur "push-forward" the measureukuran ''P'' ondina Ω tokana a measurengukur d''F'' ondina '''R'''.
TheDina underlyingkaayaan probabilityruang spaceprobabiliti Ω isngarupakeun aalat technicaltenis devicedipake usedkeur tongajamin guaranteeayana the existence ofvariabel random variables, and sometimessarta tokadang-kadang constructkeur themnyusunna. InDina practicepraktis, one often disposes of the space Ω altogether and just puts a measure on '''R''' that assigns measure 1 to the whole real line, i.e., one works with probability distributions instead of random variables.
