# 4.1 Matlab and independent classes

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In the independent case, we may calculate all minterm probabilities from the probabilities of the basic events. These calculations are straightforward, but may be tedious and subject to errors. An m-function minprob calculates all minterm probabilities from the probabilities of the basic or generating sets. To arrange these as on a minterm map, m-function minmap reshapes the row matrix pm. When minterm probabilities are available, m-function ikn(P,k) calculates individual probabilities and ckn(P,k) calculates the probabilities that k or more occur. These provide the basis of a variety of useful calculations. The m-function imintest checks a vector of minterm probabilities for feasible size, determines the number of variables, and performs a check for independence.As in the nonindependent case, we may utilize the minterm expansion and the minterm probabilities to calculate the probabilities of Boolean combinations of events. However,it is frequently more efficient to manipulate the expressions for the Boolean combination to be a disjoint union of intersections.Various Matlab calculations on independent Boolean combinations are readily performed.

## Matlab and independent classes

In the unit on Minterms , we show how to use minterm probabilities and minterm vectors to calculate probabilities of Boolean combinations of events. In Independence of Events we show that in theindependent case, we may calculate all minterm probabilities from the probabilities of the basic events. While these calculations are straightforward, they may be tedious andsubject to errors. Fortunately, in this case we have an m-function minprob which calculates all minterm probabilities from the probabilities of the basic or generating sets. This function uses the m-function mintable to set upthe patterns of p 's and q 's for the various minterms and then takes the products to obtain the set of minterm probabilities.

>>pm = minprob(0.1*[4 7 6])pm = 0.0720 0.1080 0.1680 0.2520 0.0480 0.0720 0.1120 0.1680

It may be desirable to arrange these as on a minterm map. For this we have an m-function minmap which reshapes the row matrix $pm$ , as follows:

>>t = minmap(pm) t = 0.0720 0.1680 0.0480 0.11200.1080 0.2520 0.0720 0.1680

Probability of occurrence of k of n independent events

In Example 2, we show how to use the m-functions mintable and csort to obtain the probability of the occurrence of k of n events, when minterm probabilities are available. In the case of an independent class, the minterm probabilities are calculated easilyby minprob, It is only necessary to specify the probabilities for the n basic events and the numbers k of events. The size of the class, hence the mintable, is determined, and the minterm probabilities are calculated by minprob. We have twouseful m-functions. If P is a matrix of the n individual event probabilities, and k is a matrix of integers less than or equal to n , then

$\text{function}y=\mathrm{ikn}\left(P,k\right)$ calculates individual probabilities that $k$ of $n$ occur

$\text{function}y=\mathrm{ckn}\left(P,k\right)$ calculates the probabilities that $k$ or more occur

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive