Sebaran probabilitas

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Dina matematika, sebaran probabilitas nangtukeun unggal interval tina wilangan nyata kamungkinan, mangka kitu aksioma probabilitas terpenuhi. Dina watesan teknik, probabiliti sebaran nyaeta ukuran probabilitas numana domain mangrupa aljabar Borel dina kaayaan riil.

Probabilitas sebaran dina kasus husus ngarupakeun notasi nu leuwih tina ukuran probabilitas, nyaéta fungsi nu assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.

Unggal variabel acak gives rise to a probability distribution, and this distribution contains most of the important information about the variable. If X is a random variable, the corresponding probability distribution assigns to the interval [a, b] the probability Pr[aXb], i.e. the probability that the variable X will take a value in the interval [a, b].

Sebaran probabilitas variabel X bisa sacara unik didadarkeun ku fungsi sebaran kumulatif F(x), nu ditangtukeun ku


F(x) = {\rm Pr} \left[ X \le x \right]

pikeun x anggota R.

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A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps, which means 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 means 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 integrable function f defined on the reals such that


{\rm Pr} \left[ a \le X \le b \right] = \int_a^b f(x)\,dx

for all a and b. That discrete distributions do not admit such a density is unsurprising, but there are continuous distributions like the devil's staircase that also do not admit a density.

The support of a distribution is the smallest closed set whose complement has probability zero.

Jejer penting dina sebaran probabiliti[édit | sunting sumber]

Sababaraha sebaran probabiliti kacida pentingna dina teori atawa pamakean dibere ngaran nu husus:

Tempo oge[édit | sunting sumber]

daptar jejer statistis -- variabel acak -- cumulative distribution function -- probability density function -- likelihood

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