Sebaran probabilitas: Béda antarrépisi

Dina [[matematika]], '''sebaran probabilitas''' nangtukeun unggal [[interval (matematika)|interval]] tina [[wilangan nyata]] [[kamungkinan]], mangka kitu [[aksioma probabilitas]] ''terpenuhi''. Dina watesan teknik, probabiliti sebaran nyaetanyaéta [[ukuran probabilitas]] numana domain mangrupa [[aljabar Borel]] dina kaayaan riil.

Probabilitas sebaran dina kasus husus ngarupakeunmangrupa notasi nu leuwih tina ukuran probabilitas, nyaéta fungsi nu assigns probabilities satisfying the [[Kolmogorov axioms]] to the measurableméasurable sets of a [[aljabar sigma|measurable space]].

pikeun ''x'' anggota '''R'''.

A distribution is called ''discrete'' if its cumulative distribution function consists of a sequence of finite jumps, which meansméans that it belongs to a [[discrete random variable]] ''X'': a variable which can only attain values from a certain finite or [[countable]] set.

A distribution is called ''continuous'' if its cumulative distribution function is [[continuous]], which meansméans that it belongs to a random variable ''X'' for which Pr[ ''X'' = ''x'' ] = 0 for all ''x'' in '''R'''.

The so-called ''absolutely continuous distributions'' can be expressed by a [[fungsi dénsitas probabilitas]]: a non-negative [[Lebesgue integration|Lebesgue integrable]] function ''f'' defined on the realsréals such that

Sababaraha sebaran probabiliti kacida pentingna dina teoritéori atawa pamakeanpamakéan dibere ngaran nu husus:

*** [[degenerate distribution|Sebaran ''degenerate'']] dina ''x''₀, numana ''X'' ngarupakeunmangrupa nilai penting dicokot jadi nilai ''x₀''. This does not look random, but it satisfies the definition of [[variabel acak]]. This is useful because it puts deterministic variables and random variables in the same formalism.

*** The discrete [[sebaran seragam|uniform distribution]], where all elements of a finite [[set theory|set]] are equally likely. This is supposed to be the distribution of a balanced coin, an unbiased die, a casino roulette or a well-shuffled deck. Also, one can use measurementsméasurements of quantum states to generate uniform random variables. All these are "physical" or "mechanical" devices, subject to design flaws or perturbations, so the uniform distribution is only an approximation of their behaviour. In digital computers, [[Pseudorandom number sequence|pseudo-random number generators]] are used to produced a [[randomness|statistically random]] discrete uniform distribution.

*** The [[negative binomial distribution]], a generalization of the geometricgéometric distribution to the ''n''th success.

*** The [[zeta distribution]] has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theoriststhéorists.

*** [[sebaran seragam]] dina [''a'',''b''], numana sakabehsakabéh titik dina interval nu kawengku mibanda ajen nu ampir sarua.

*** [[Sebaran beta]] dina [0,1], ngarupakeunmangrupa sebaran seragam dina kasus husus, nu dipakedipaké dina estimasi probabiliti sukses.

*** [[Sebaran chi-kuadrat]], nu ngarupakeunmangrupa jumlah kuadrat ''n'' variabel random Gauss bebas. Ieu ngarupakeunmangrupa kasus husus dina sebaran Gamma, sarta dipakedipaké dina tes goodness-of-fit dina [[statistik]].

*** [[Sebaran-F]], numana sebaran rasio dua sebaran variabel normal, dipakedipaké dina [[analisa varian]].

** Supported on the whole realréal line

*** [[Sebaran normal]], disebut ogeogé Gaussian atawa kurva bel. It is ubiquitous in nature and statistics due to the [[central limit theorem]]: every variable that can be modelled as a sum of many small independent variables is approximately normal.

*** [[Sebaran-t student]], dipakedipaké keur nga-''estimasi'' meanméan nu teu dipikanyaho dina populasi ''Gaussian''.

*** [[Sebaran Cauchy]], conto sebaran nu teu ngabogaan [[nilai ekspektasi]] atawa [[varian]]. Dina fisika biasana disebut Lorentzian, sarta ieu sebaran tina tetapan energiénérgi teu stabil dina mekanika kuantum. Dina fisika partikel, the extremely short-lived particles associated to such unstable states are called [[resonance]]s.