Fundamentals of Probability and Stochastic Processes with Applications to Communications by Kun Il Park

Author:Kun Il Park
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(5.80)

Ω c contains 2 n elementary events, which are ordered n-tuples of S and F. For example, for n = 2, Ω c = {(SS), (SF), (FS), (FF)} and the elementary events are {(SS)}, {(SF)}, {(FS)}, and {(FF)}.

The probabilities of the elementary events in Ω c are as follows:

(5.81)

There is one unique elementary event corresponding to k successes in a specific order. The probability of this elementary event is p k (1−p) n−k . There are elementary events with k successes in any order. Since the elementary events are mutually exclusive , the probability of k successes in any order is equal to the sum of the probabilities of these k elementary events. Hence, the RV X is binomially distributed with the pdf and the CDF given by (5.68) and (5.69), respectively.

The following examples illustrate the experiments that belong to the class of the Bernoulli trial .

Example 5.4.1

Consider a digital connection with three links. The probability of an error on each link is assumed to be p. A digital bit 0 is transmitted from the source to the destination over the three links. Find the end-to-end probability that the bit 0 will arrive as bit 0.

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