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[1] [5] In other words, the geometric random variable is the only discrete memoryless distribution and the exponential random variable is the only continuous memoryless distribution.
A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past.
Degenerate distribution: A deterministic or fixed service time. M/D/1 queue: E k: Erlang distribution: An Erlang distribution with k as the shape parameter (i.e., sum of k i.i.d. exponential random variables). G: General distribution: Although G usually refers to independent service time, some authors prefer to use GI to be explicit. M/G/1 ...
The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution. [1]: 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.
A discrete memoryless single-relay channel can be modelled as four finite sets, ,,, and , and a conditional probability distribution (, |,) on these sets. The probability distribution of the choice of symbols selected by the encoder and the relay encoder is represented by p ( x 1 , x 2 ) {\displaystyle p(x_{1},x_{2})} .
For an exponential survival distribution, the probability of failure is the same in every time interval, no matter the age of the individual or device. This fact leads to the "memoryless" property of the exponential survival distribution: the age of a subject has no effect on the probability of failure in the next time interval.
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function It has the cumulative distribution function
(This formula is sometimes called the Hartley function.) This is the maximum possible rate of information that can be transmitted with that alphabet. (The logarithm should be taken to a base appropriate for the unit of measurement in use.) The absolute rate is equal to the actual rate if the source is memoryless and has a uniform distribution.