The focus of this course is on digital communication, which
involves transmission of information, in its most general sense,from source to destination using digital technology.
Engineering such a system requires modeling both the informationand the transmission media. Interestingly, modeling both digital
or analog information and many physical media requires aprobabilistic setting. In this chapter and in the next one we
will review the theory of probability, model random signals, andcharacterize their behavior as they traverse through
deterministic systems disturbed by noise and interference. Inorder to develop practical models for random phenomena we start
with carrying out a random experiment. We then introducedefinitions, rules, and axioms for modeling within the context
of the experiment. The outcome of a random experiment isdenoted by
$$ . The sample
space
$$ is the set of
all possible outcomes of a random experiment. Such outcomescould be an abstract description in words. A scientific
experiment should indeed be repeatable where each outcome couldnaturally have an associated probability of occurrence. This is
defined formally as the ratio of the number of times the outcomeoccurs to the total number of times the experiment is repeated.
Random variables
A random variable is the assignment of a real number to each
outcome of a random experiment.
Roll a dice. Outcomes
$\{{}_{1}, {}_{2}, {}_{3}, {}_{4}, {}_{5}, {}_{6}\}$
The cumulative distribution function of a random variable
$X$ is a function
$F(X, (\mathbb{R}, \mathbb{R}))$ such that
$$F(X, b)=(X\le b)=(\{\in \colon X()\le b\})$$
Continuous Random Variable
A random variable
$X$ is
continuous if the cumulative distribution function can bewritten in an integral form, or
$$F(X, b)=\int_{()} \,d x$$∞bfXx
and
$f(X, x)$ is the probability density function (pdf) (
e.g. ,
$F(X, x)$ is differentiable and
$f(X, x)=\frac{d F(X, x)}{d x}$ )
Discrete Random Variable
A random variable
$X$ is
discrete if it only takes at most countably many points(
i.e. ,
$F(X, )$ is piecewise constant). The probability mass function (pmf) is
defined as
$${R}_{XY}=\langle X{Y}^{*}\rangle =\begin{cases}\int_{()} \,d y & \text{if $$}\end{cases}$$∞∞x∞∞xy*fXYxyX and Y are jointly continuouskkllxkyl*pXYxkylX and Y are jointly discrete
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?