# Appendix a to applied probability: directory of m-functions and m  (Page 22/24)

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## Compound demand

The following pattern provides a useful model in many situations. Consider

$D=\sum _{k=0}^{N}{Y}_{k}$

where ${Y}_{0}=0$ , and the class $\left\{{Y}_{k}:1\le k\right\}$ is iid, independent of the counting random variable N . One natural interpretation is to consider N to be the number of customers in a store and Y k the amount purchased by the k th customer. Then D is the total demand of the actual customers. Hence, we call D the compound demand .

gend.m Uses coefficients of the generating functions for N and Y to calculate, in the integer case, the marginal distribution for the compound demand D and the joint distribution for $\left\{N,D\right\}$ .

% GEND file gend.m Marginal and joint dbn for integer compound demand % Version of 5/21/97% Calculates marginal distribution for compound demand D % and joint distribution for {N,D} in the integer case% Do not forget zero coefficients for missing powers % in the generating functions for N, Ydisp('Do not forget zero coefficients for missing powers') gn = input('Enter gen fn COEFFICIENTS for gN ');gy = input('Enter gen fn COEFFICIENTS for gY '); n = length(gn) - 1; % Highest power in gNm = length(gy) - 1; % Highest power in gY P = zeros(n + 1,n*m + 1); % Base for generating Py = 1; % Initialization P(1,1) = gn(1); % First row of P (P(N=0) in the first position)for i = 1:n % Row by row determination of P y = conv(y,gy); % Successive powers of gyP(i+1,1:i*m+1) = y*gn(i+1); % Successive rows of P endPD = sum(P); % Probability for each possible value of D a = find(gn); % Location of nonzero N probabilitiesb = find(PD); % Location of nonzero D probabilities P = P(a,b); % Removal of zero rows and columnsP = rot90(P); % Orientation as on the plane N = 0:n;N = N(a); % N values with positive probabilites PN = gn(a); % Positive N probabilitiesY = 0:m; % All possible values of Y Y = Y(find(gy)); % Y values with positive probabilitiesPY = gy(find(gy)); % Positive Y proabilities D = 0:n*m; % All possible values of DPD = PD(b); % Positive D probabilities D = D(b); % D values with positive probabilitiesgD = [D; PD]'; % Display combinationdisp('Results are in N, PN, Y, PY, D, PD, P') disp('May use jcalc or jcalcf on N, D, P')disp('To view distribution for D, call for gD')

gendf.m function [d,pd] = gendf(gn,gy) is a function version of gend , which allows arbitrary naming of the variables. Calculates the distribution for D , but not the joint distribution for $\left\{N,D\right\}$ .

function [d,pd] = gendf(gn,gy)% GENDF [d,pd] = gendf(gN,gY) Function version of gend.m% Calculates marginal for D in the integer case % Version of 5/21/97% Do not forget zero coefficients for missing powers % in the generating functions for N, Yn = length(gn) - 1; % Highest power in gN m = length(gy) - 1; % Highest power in gYP = zeros(n + 1,n*m + 1); % Base for generating P y = 1; % InitializationP(1,1) = gn(1); % First row of P (P(N=0) in the first position) for i = 1:n % Row by row determination of Py = conv(y,gy); % Successive powers of gy P(i+1,1:i*m+1) = y*gn(i+1); % Successive rows of Pend PD = sum(P); % Probability for each possible value of DD = 0:n*m; % All possible values of D b = find(PD); % Location of nonzero D probabilitiesd = D(b); % D values with positive probabilities pd = PD(b); % Positive D probabilities

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
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
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
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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
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive