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In the asymptotic setting, a family of deterministic polynomial time computable functions : {,} {,} for some polynomial p, is a pseudorandom number generator (PRNG, or PRG in some references), if it stretches the length of its input (() > for any k), and if its output is computationally indistinguishable from true randomness, i.e. for any probabilistic polynomial time algorithm A, which ...
ExpressVPN was founded in 2009 by Peter Burchhardt and Dan Pomerantz, two serial entrepreneurs who were also Wharton School alumni. [6]In July 2017, ExpressVPN announced in an open letter and later a public statement by Apple, that Apple had removed all VPN apps from its App Store in China, a revelation that was later picked up by The New York Times and other news outlets.
The probability generating function of a binomial random variable, the number of successes in trials, with probability of success in each trial, is () = [() +]. Note : it is the n {\displaystyle n} -fold product of the probability generating function of a Bernoulli random variable with parameter p {\displaystyle p} .
A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount; Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution; Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS ...
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In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.