# Appendix a to applied probability: directory of m-functions and m  (Page 9/24)

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trialmatch.m Estimates the probability of matches in n independent trials from identical distributions. The sample size and number of trials mustbe kept relateively small to avoid exceeding available memory.

% TRIALMATCH file trialmatch.m Estimates probability of matches % in n independent trials from identical distributions% Version of 8/20/97 % Estimates the probability of one or more matches% in a random selection from n identical distributions % with a small number of possible values% Produces a supersample of size N = n*ns, where % ns is the number of samples. Samples are separated.% Each sample is sorted, and then tested for differences % between adjacent elements. Matches are indicated by% zero differences between adjacent elements in sorted sample. X = input('Enter the VALUES in the distribution ');PX = input('Enter the PROBABILITIES '); c = length(X);n = input('Enter the SAMPLE SIZE n '); ns = input('Enter the number ns of sample runs ');N = n*ns; % Length of supersample U = rand(1,N); % Vector of N random numbersT = dquant(X,PX,U); % Supersample obtained with quantile function; % the function dquant determines quantile% function values for random number sequence U ex = sum(T)/N; % Sample averageEX = dot(X,PX); % Population mean vx = sum(T.^2)/N - ex^2; % Sample varianceVX = dot(X.^2,PX) - EX^2; % Population variance A = reshape(T,n,ns); % Chops supersample into ns samples of size nDS = diff(sort(A)); % Sorts each sample m = sum(DS==0)>0; % Differences between elements in each sample % -- Zero difference iff there is a matchpm = sum(m)/ns; % Fraction of samples with one or more matches d = arrep(c,n);p = PX(d); p = reshape(p,size(d)); % This step not needed in version 5.1ds = diff(sort(d))==0; mm = sum(ds)>0; m0 = find(1-mm);pm0 = p(:,m0); % Probabilities for arrangements with no matches P0 = sum(prod(pm0));disp('The sample is in column vector T') % Displays of results disp(['Sample average ex = ', num2str(ex),]) disp(['Population mean E(X) = ',num2str(EX),]) disp(['Sample variance vx = ',num2str(vx),]) disp(['Population variance V(X) = ',num2str(VX),]) disp(['Fraction of samples with one or more matches pm = ', num2str(pm),]) disp(['Probability of one or more matches in a sample Pm = ', num2str(1-P0),])

## Distributions

comb.m function y = comb(n,k) Calculates binomial coefficients. k may be a matrix of integers between 0 and n . The result y is a matrix of the same dimensions.

function y = comb(n,k) % COMB y = comb(n,k) Binomial coefficients% Version of 12/10/92 % Computes binomial coefficients C(n,k)% k may be a matrix of integers between 0 and n % result y is a matrix of the same dimensionsy = round(gamma(n+1)./(gamma(k + 1).*gamma(n + 1 - k)));

ibinom.m Binomial distribution — individual terms. We have two m-functions ibinom and cbinom for calculating individual and cumulative terms, $P\left({S}_{n}=k\right)$ and $P\left({S}_{n}\ge k\right)$ , respectively.

$P\left({S}_{n}=k\right)=C\left(n,\phantom{\rule{0.166667em}{0ex}}k\right){p}^{k}{\left(1-p\right)}^{n-k}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\text{and}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}P\left({S}_{n}\ge k\right)=\sum _{r=k}^{n}P\left({S}_{n}=r\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}0\le k\le n$
For these m-functions, we use a modification of a computation strategy employed by S. Weintraub: Tables of the Cumulative Binomial Probability Distribution for Small Values of p , 1963. The book contains a particularly helpful error analysis, written by Leo J. Cohen. Experimentation with sums and expectations indicates aprecision for ibinom and cbinom calculations that is better than ${10}^{-10}$ for $n=1000$ and p from 0.01 to 0.99. A similar precision holds for values of n up to 5000, provided $np$ or $nq$ are limited to approximately 500. Above this value for $np$ or $nq$ , the computations break down. For individual terms, function y = ibinom(n,p,k) calculates the probabilities for n a positive integer, k a matrix of integers between 0 and n . The output is a matrix of the corresponding binomial probabilities.

function y = ibinom(n,p,k) % IBINOM y = ibinom(n,p,k) Individual binomial probabilities% Version of 10/5/93 % n is a positive integer; p is a probability% k a matrix of integers between 0 and n % y = P(X>=k) (a matrix of probabilities) if p>0.5 a = [1 ((1-p)/p)*ones(1,n)]; b = [1 n:-1:1]; c = [1 1:n]; br = (p^n)*cumprod(a.*b./c);bi = fliplr(br); elsea = [1 (p/(1-p))*ones(1,n)];b = [1 n:-1:1];c = [1 1:n];bi = ((1-p)^n)*cumprod(a.*b./c); endy = bi(k+1);

#### Questions & Answers

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
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
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
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?
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
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