# Appendix a to applied probability: directory of m-functions and m  (Page 18/24)

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japprox.m Assumes discrete setup and calculates basic quantities for a pair of random variables as in jsimple. Plots the regression line and regression curve.

% JAPPROX file japprox.m Basic quantities for ac pair {X,Y} % Version of 5/7/96% Assumes tuappr has set X, Y, PX, PY, t, u, P EX = total(t.*P) % E[X]EY = total(u.*P) % E[Y] EX2 = total(t.^2.*P) % E[X^2]EY2 = total(u.^2.*P) % E[Y^2] EXY = total(t.*u.*P) % E[XY]VX = EX2 - EX^2 % Var[X] VY = EY2 - EY^2 % Var[Y]cv = EXY - EX*EY; % Cov[X,Y] = E[XY]- E[X]E[Y]if abs(cv)>1e-9 % to prevent roundoff error masking zero CV = cvelse CV = 0end a = CV/VX % regression line of Y on X isb = EY - a*EX % u = at + b R = CV/sqrt(VX*VY);disp(['The regression line of Y on X is: u = ',num2str(a),'t + ',num2str(b),])disp(['The correlation coefficient is: rho = ',num2str(R),])disp(' ') eY = sum(u.*P)./sum(P); % eY(t) = E[Y|X = t]RL = a*X + b; plot(X,RL,X,eY,'-.')grid title('Regression line and Regression curve')xlabel('X values') ylabel('Y values')legend('Regression line','Regression curve') clear eY % To conserve memoryclear RL disp('Calculate with X, Y, t, u, P, as in joint simple case')

## Calculations and tests for independent random variables

mgsum.m function [z,pz] = mgsum(x,y,px,py) determines the distribution for the sum of an independent pair of simple random variables from their distributions.

function [z,pz] = mgsum(x,y,px,py)% MGSUM [z,pz] = mgsum(x,y,px,py) Sum of two independent simple rv% Version of 5/6/96 % Distribution for the sum of two independent simple random variables% x is a vector (row or column) of X values % y is a vector (row or column) of Y values% px is a vector (row or column) of X probabilities % py is a vector (row or column) of Y probabilities% z and pz are row vectors [a,b]= meshgrid(x,y); t = a+b;[c,d] = meshgrid(px,py);p = c.*d; [z,pz]= csort(t,p);

mgsum3.m function [w,pw] = mgsum3(x,y,z,px,py,pz) extends mgsum to three random variables by repeated application of mgsum. Similarly for mgsum4.m.

function [w,pw] = mgsum3(x,y,z,px,py,pz)% MGSUM3 [w,pw] = mgsum3(x,y,z,px,py,y) Sum of three independent simple rv% Version of 5/2/96 % Distribution for the sum of three independent simple random variables% x is a vector (row or column) of X values % y is a vector (row or column) of Y values% z is a vector (row or column) of Z values % px is a vector (row or column) of X probabilities% py is a vector (row or column) of Y probabilities % pz is a vector (row or column) of Z probabilities% W and pW are row vectors [a,pa]= mgsum(x,y,px,py); [w,pw]= mgsum(a,z,pa,pz);

mgnsum.m function [z,pz] = mgnsum(X,P) determines the distribution for a sum of n independent random variables. X an n -row matrix of X -values and  P an n -row matrix of P -values (padded with zeros, if necessary, to make all rows the same length.

function [z,pz] = mgnsum(X,P)% MGNSUM [z,pz] = mgnsum(X,P) Sum of n independent simple rv% Version of 5/16/96 % Distribution for the sum of n independent simple random variables% X an n-row matrix of X-values % P an n-row matrix of P-values% padded with zeros, if necessary % to make all rows the same length[n,r] = size(P);z = 0; pz = 1;for i = 1:n x = X(i,:);p = P(i,:);x = x(find(p>0)); p = p(find(p>0)); [z,pz]= mgsum(z,x,pz,p); end

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
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