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* The [[cache language model]]s and other [[Statistical Language Model|statistical language models]] used in [[natural language processing]] to assign probabilities to the occurrence of particular words and word sequences do so by means of probability distributions.

* The [[cache language model]]s and other [[Statistical Language Model|statistical language models]] used in [[natural language processing]] to assign probabilities to the occurrence of particular words and word sequences do so by means of probability distributions.

在自然语言处理中使用的高速缓存语言模型和其他统计语言模型通过概率分布来为特定单词和单词序列的出现分配概率。

在自然语言处理中使用的高速缓存语言模型和其他统计语言模型通过概率分布来为特定单词和单词序列的出现分配概率。

 

* In quantum mechanics, the probability density of finding the particle at a given point is proportional to the square of the magnitude of the particle's [[wavefunction]] at that point (see [[Born rule]]). Therefore, the probability distribution function of the position of a particle is described by <math>P_{a\le x\le b} (t) = \int_a^b d x\,|\Psi(x,t)|^2 </math>, probability that the particle's position {{math|''x''}} will be in the interval {{math|''a'' ≤ ''x'' ≤ ''b''}} in dimension one, and a similar [[triple integral]] in dimension three. This is a key principle of quantum mechanics.<ref>{{Cite book|title=Physical chemistry for the chemical sciences|last=Chang, Raymond.|publisher=|others=Thoman, John W., Jr., 1960-|year=|isbn=978-1-68015-835-9|location=[Mill Valley, California]|pages=403–406|oclc=927509011}}</ref>

* In quantum mechanics, the probability density of finding the particle at a given point is proportional to the square of the magnitude of the particle's [[wavefunction]] at that point (see [[Born rule]]). Therefore, the probability distribution function of the position of a particle is described by <math>P_{a\le x\le b} (t) = \int_a^b d x\,|\Psi(x,t)|^2 </math>, probability that the particle's position {{math|''x''}} will be in the interval {{math|''a'' ≤ ''x'' ≤ ''b''}} in dimension one, and a similar [[triple integral]] in dimension three. This is a key principle of quantum mechanics.<ref>{{Cite book|title=Physical chemistry for the chemical sciences|last=Chang, Raymond.|publisher=|others=Thoman, John W., Jr., 1960-|year=|isbn=978-1-68015-835-9|location=[Mill Valley, California]|pages=403–406|oclc=927509011}}</ref>

在量子力学中，在给定点处找到粒子的概率密度与该点处粒子波函数大小的平方成正比（请参阅博恩法则）。因此，粒子位置的概率分布函数描述为<math>P_{a\le x\le b} (t) = \int_a^b d x\,|\Psi(x,t)|^2 </math>，粒子位置的概率x在第一个维度中的间隔为a≤x≤b，在第三个维度中的间隔类似。这是量子力学的关键原理。

在量子力学中，在给定点处找到粒子的概率密度与该点处粒子波函数大小的平方成正比（请参阅博恩法则）。因此，粒子位置的概率分布函数描述为<math>P_{a\le x\le b} (t) = \int_a^b d x\,|\Psi(x,t)|^2 </math>，粒子位置的概率x在第一个维度中的间隔为a≤x≤b，在第三个维度中的间隔类似。这是量子力学的关键原理。

* [[List of statistical topics]]

* [[List of statistical topics]]

统计学话题的清淡

统计学话题的清淡

=== Probability distributions 概率分布 ===

=== Probability distributions 概率分布 ===