# Appendix a to applied probability: directory of m-functions and m  (Page 19/24)

 Page 19 / 24

mgsumn.m function [z,pz] = mgsumn(varargin) is an alternate to mgnsum, utilizing varargin in MATLAB version 5.1. The call is of the form [z,pz] = mgsumn([x1;p1],[x2;p2], ..., [xn;pn]) .

function [z,pz] = mgsumn(varargin)% MGSUMN [z,pz] = mgsumn([x1;p1],[x2;p2], ..., [xn;pn]) % Version of 6/2/97 Uses MATLAB version 5.1% Sum of n independent simple random variables % Utilizes distributions in the form [x;px](two rows) % Iterates mgsumn = length(varargin); % The number of distributions z = 0; % Initializationpz = 1; for i = 1:n % Repeated use of mgsum[z,pz] = mgsum(z,varargin{i}(1,:),pz,varargin{i}(2,:));end

diidsum.m function [x,px] = diidsum(X,PX,n) determines the sum of n iid simple random variables, with the common distribution $X,PX$ .

function [x,px] = diidsum(X,PX,n)% DIIDSUM [x,px] = diidsum(X,PX,n) Sum of n iid simple random variables% Version of 10/14/95 Input rev 5/13/97 % Sum of n iid rv with common distribution X, PX% Uses m-function mgsum x = X; % Initializationpx = PX; for i = 1:n-1[x,px] = mgsum(x,X,px,PX);end

itest.m Tests for independence the matrix P of joint probabilities for a simple pair $\left\{X,Y\right\}$ of random variables.

% ITEST file itest.m Tests P for independence % Version of 5/9/95% Tests for independence the matrix of joint % probabilities for a simple pair {X,Y}pt = input('Enter matrix of joint probabilities '); disp(' ')px = sum(pt); % Marginal probabilities for X py = sum(pt'); % Marginal probabilities for Y (reversed)[a,b] = meshgrid(px,py);PT = a.*b; % Joint independent probabilities D = abs(pt - PT)>1e-9; % Threshold set above roundoff if total(D)>0 disp('The pair {X,Y} is NOT independent')disp('To see where the product rule fails, call for D') elsedisp('The pair {X,Y} is independent') end

idbn.m function p = idbn(px,py) uses marginal probabilities to determine the joint probability matrix (arranged as on the plane) for an independent pair of simple randomvariables.

function p = idbn(px,py) % IDBN p = idbn(px,py) Matrix of joint independent probabilities% Version of 5/9/95 % Determines joint probability matrix for two independent% simple random variables (arranged as on the plane) [a,b]= meshgrid(px,fliplr(py)); p = a.*b

isimple.m Takes as inputs the marginal distributions for an independent pair $\left\{X,Y\right\}$ of simple random variables. Sets up the joint distribution probability matrix P as in idbn , and forms the calculating matrices $t,u$ as in jcalc . Calculates basic quantities and makes available matrices $X,Y,PX,PY,P,t,u$ for additional calculations.

% ISIMPLE file isimple.m Calculations for independent simple rv % Version of 5/3/95X = input('Enter row matrix of X-values '); Y = input('Enter row matrix of Y-values ');PX = input('Enter X probabilities '); PY = input('Enter Y probabilities ');[a,b] = meshgrid(PX,fliplr(PY));P = a.*b; % Matrix of joint independent probabilities [t,u]= meshgrid(X,fliplr(Y)); % t, u matrices for joint calculations EX = dot(X,PX) % E[X]EY = dot(Y,PY) % E[Y] VX = dot(X.^2,PX) - EX^2 % Var[X]VY = dot(Y.^2,PY) - EY^2 % Var[Y] disp(' Use array operations on matrices X, Y, PX, PY, t, u, and P')

#### Questions & Answers

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
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
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive