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
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?