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This page was last edited on 1 November 2019, at 22:44 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
On average the computation discards proportion p 2 + (1 − p) 2 of the input pairs(00 and 11), which is near one when p is near zero or one, and is minimized at 1/4 when p = 1/2 for the original process (in which case the output stream is 1/4 the length of the input stream on average).
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
The first AP Physics 1 classes had begun in the 2014–2015 school year, with the first AP exams administered in May 2015. In its first five years, AP Physics 1 covered forces and motion, conservation laws, waves, and electricity. [4] As of 2021, AP Physics 1 includes mechanics topics only. [5]
The length of the arc is 5/6 of the length of the circle, which is why the conditional probability is equal to 5/6. This successful geometric explanation may create the illusion that the following question is trivial. A point of a given sphere is chosen at random (uniformly).
Here, E is a function from the space of states to the real numbers; in physics applications, E(x) is interpreted as the energy of the configuration x. The parameter β is a free parameter; in physics, it is the inverse temperature. The normalizing constant Z(β) is the partition function. However, in infinite systems, the total energy is no ...