# Appendix a to applied probability: directory of m-functions and m  (Page 20/24)

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## Quantile functions for bounded distributions

dquant.m function t = dquant(X,PX,U) determines the values of the quantile function for a simple random variable with distribution $X,PX$ at the probability values in row vector U . The probability vector U is often determined by a random number generator.

function t = dquant(X,PX,U) % DQUANT t = dquant(X,PX,U) Quantile function for a simple random variable% Version of 10/14/95 % U is a vector of probabilitiesm = length(X); n = length(U);F = [0 cumsum(PX)+1e-12];F(m+1) = 1; % Makes maximum value exactly one if U(n)>= 1 % Prevents improper values of probability U U(n) = 1;end if U(1)<= 0 U(1) = 1e-9;end f = rowcopy(F,n); % n rows of Fu = colcopy(U,m); % m columns of U t = X*((f(:,1:m)<u)&(u<= f(:,2:m+1)))';

dquanplot.m Plots as a stairs graph the quantile function for a simple random variable X . The plot is the values of X versus the distribution function F X .

% DQUANPLOT file dquanplot.m Plot of quantile function for a simple rv % Version of 7/6/95% Uses stairs to plot the inverse of FX X = input('Enter VALUES for X ');PX = input('Enter PROBABILITIES for X '); m = length(X);F = [0 cumsum(PX)];XP = [X X(m)];stairs(F,XP) gridtitle('Plot of Quantile Function') xlabel('u')ylabel('t = Q(u)') hold onplot(F(2:m+1),X,'o') % Marks values at jumps hold off

dsample.m Calculates a sample from a discrete distribution, determines the relative frequencies of values, and compares with actual probabilities. Input consists of value andprobability matrices for X and the sample size n . A matrix U is determined by a random number generator, and the m-function dquant is used to calculate the corresponding sample values. Variousdata on the sample are calculated and displayed.

% DSAMPLE file dsample.m Simulates sample from discrete population % Version of 12/31/95 (Display revised 3/24/97)% Relative frequencies vs probabilities for % sample from discrete population distributionX = input('Enter row matrix of VALUES '); PX = input('Enter row matrix of PROBABILITIES ');n = input('Sample size n '); U = rand(1,n);T = dquant(X,PX,U); [x,fr]= csort(T,ones(1,length(T))); disp(' Value Prob Rel freq')disp([x; PX; fr/n]')ex = sum(T)/n; EX = dot(X,PX);vx = sum(T.^2)/n - ex^2; VX = dot(X.^2,PX) - EX^2;disp(['Sample average ex = ',num2str(ex),])disp(['Population mean E[X] = ',num2str(EX),]) disp(['Sample variance vx = ',num2str(vx),]) disp(['Population variance Var[X]= ',num2str(VX),])

quanplot.m Plots the quantile function for a distribution function F X . Assumes the procedure dfsetup or acsetup has been run. A suitable set U of probability values is determined and the m-function dquant is used to determine corresponding values of the quantile function. The results are plotted.

% QUANPLOT file quanplot.m Plots quantile function for dbn function % Version of 2/2/96% Assumes dfsetup or acsetup has been run % Uses m-function dquantX = input('Enter row matrix of values '); PX = input('Enter row matrix of probabilities ');h = input('Probability increment h '); U = h:h:1;T = dquant(X,PX,U); U = [0 U 1]; Te = X(m) + abs(X(m))/20;T = [X(1) T Te];plot(U,T) % Plot rather than stairs for general case gridtitle('Plot of Quantile Function') xlabel('u')ylabel('t = Q(u)')

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
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
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 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