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10+2 is a children's animated series from Catalonia (Spain), produced by Accio Studios and Victory Media Group, and directed by Miquel Pujol i Lozano. The show debuted in 1991. The show debuted in 1991.
In statistical hypothesis testing, a turning point test is a statistical test of the independence of a series of random variables. [1] [2] [3] Maurice Kendall and Alan Stuart describe the test as "reasonable for a test against cyclicity but poor as a test against trend." [4] [5] The test was first published by Irénée-Jules Bienaymé in 1874 ...
In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions.
The Dirac comb of period 2 π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta function. It represents a discrete probability distribution concentrated at 2 π n — a degenerate distribution — but the notation treats it as if it were a continuous distribution.
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Axiomatic probability theory deliberately avoids a definition of a random sequence. [2] Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness.
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to ...
For example, if you have two choices, one with probability 0.9, your chances of a correct guess using the optimal strategy are 90 percent. Yet, the perplexity is 2 −0.9 log 2 0.9 - 0.1 log 2 0.1 = 1.38. The inverse of the perplexity, 1/1.38 = 0.72, does not correspond to the 0.9 probability.