Elementary Probability Theory - Digital Communication: Principles and System Modelling - page 206

Appendix A
Elementary Probability Theory
A.1 Concept of Probability
In communication system, prediction of system performance, noise accumula-
tion probability, probability distribution of noise are really essential studies. At a
particular instant, one physical experiment may have a deterministic outcome or in-
deterministic outcome. In this appendix, the mathematical models of experiments
are prepared. A single performance of the physical experiment is called as trial for
whichthereisan outcome .
A.1.1 Random Experiments and Sample Space
The experiments, in which results are not being essentially the same even though
conditions may be nearly identical, are called random experiments .
The following are some examples.
(a) Tossing a coin : The result of the experiment is that it will either come up 'tails,'
symbolized by T (or 0), or 'heads,' symbolized by H (or 1), i.e. one of the
elements of the set {H, T} (or {0, 1}).
(b) Tossing a die : The result of the experiment is that it will come up with one of
the numbers in the set {1, 2, 3, 4, 5, 6}.
(c) Tossing a coin twice : The results can be indicated by {HH, HT, TH, TT}, i.e.
both heads, head on first and tail on second, etc.
A set S which consists of all possible outcomes of a random experiment is called
a sample space and each outcome is called a sample point [1].
To understand sample space, let's take the example of tossing a die, one sample
space or set of all possible outcomes is given by {1, 2, 3, 4, 5, 6} while another is
{odd, even}.
If the sample space S is a set of finite number of elements, then the space is
discrete sample space like tossing a die or a coin. There are sample spaces where