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The only memoryless continuous probability distribution is the exponential distribution, shown in the following proof: [9] First, define S ( t ) = Pr ( X > t ) {\displaystyle S(t)=\Pr(X>t)} , also known as the distribution's survival function .
The memoryless Poisson distribution is the predominant model used for analyzing traffic in traditional telephony networks. The Poisson process is characterized as a renewal process. In a Poisson process the inter-arrival times are exponentially distributed with a rate parameter λ: P{An ≤ t} = 1 – exp(-λt).
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})} .
The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory, it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input. A channel model may either be digital or analog.
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 ...
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Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. The cost is a fixed, higher forward channel bandwidth. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code .
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