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Binomial, poisson, and gaussian dstributions

bincomp.m Graphical comparison of the binomial, Poisson, and Gaussian distributions. The procedure calls for binomial parameters n , p , determines a reasonable range of evaluation points and plots on the same graph the binomial distribution function, thePoisson distribution function, and the gaussian distribution function with the adjustment called the “continuity correction.”

% BINCOMP file bincomp.m Approx of binomial by Poisson and gaussian % Version of 5/24/96% Gaussian adjusted for "continuity correction" % Plots distribution functions for specified parameters n, pn = input('Enter the parameter n '); p = input('Enter the parameter p ');a = floor(n*p-2*sqrt(n*p)); a = max(a,1); % Prevents zero or negative indicesb = floor(n*p+2*sqrt(n*p)); k = a:b;Fb = cumsum(ibinom(n,p,0:n)); % Binomial distribution function Fp = cumsum(ipoisson(n*p,0:n)); % Poisson distribution functionFg = gaussian(n*p,n*p*(1 - p),k+0.5); % Gaussian distribution function stairs(k,Fb(k+1)) % Plotting detailshold on plot(k,Fp(k+1),'-.',k,Fg,'o')hold off xlabel('t values') % Graph labeling detailsylabel('Distribution function') title('Approximation of Binomial by Poisson and Gaussian')grid legend('Binomial','Poisson','Adjusted Gaussian')disp('See Figure for results')
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poissapp.m Graphical comparison of the Poisson and Gaussian distributions. The procedure calls for a value of the Poisson parameter mu, then calculates and plots the Poissondistribution function, the Gaussian distribution function, and the adjusted Gaussian distribution function.

% POISSAPP file poissapp.m Comparison of Poisson and gaussian % Version of 5/24/96% Plots distribution functions for specified parameter mu mu = input('Enter the parameter mu ');n = floor(1.5*mu); k = floor(mu-2*sqrt(mu)):floor(mu+2*sqrt(mu));FP = cumsum(ipoisson(mu,0:n)); FG = gaussian(mu,mu,k);FC = gaussian(mu,mu,k-0.5); stairs(k,FP(k))hold on plot(k,FG,'-.',k,FC,'o')hold off gridxlabel('t values') ylabel('Distribution function')title('Gaussian Approximation to Poisson Distribution') legend('Poisson','Gaussian','Adjusted Gaussian')disp('See Figure for results')
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Setup for simple random variables

If a simple random variable X is in canonical form, the distribution consists of the coefficients of the indicator funtions (the values of X ) and the probabilities of the corresponding events. If X is in a primitive form other than canonical, the csort operation is applied to the coefficients of the indicator functions and the probabilities of the corresponding events to obtainthe distribution. If Z = g ( X ) and X is in a primitive form, then the value of Z on the event in the partition associated with t i is g ( t i ) . The distribution for Z is obtained by applying csort to the g ( t i ) and the p i . Similarly, if Z = g ( X , Y ) and the joint distribution is available, the value g ( t i , u j ) is associated with P ( X = t i , Y = u j ) . The distribution for Z is obtained by applying csort to the matrix of values and the corresponding matrix of probabilities.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive
Samson Reply

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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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