# 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

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
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
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
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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