



The number
N of “hits” in a day on a Web site on the internet is
Poisson (80). Suppose the probability is 0.10 that any hit results in a sale, is 0.30that the result is a request for information, and is 0.60 that the inquirer just browses
but does not identify an interest. What is the probability of 10 or more sales? Whatis the probability that the number of sales is at least half the number of information
requests (use suitable simple approximations)?
X = 0:30;
Y = 0:80;PX = ipoisson(80*0.1,X);
PY = ipoisson(80*0.3,Y);icalc: X Y PX PY
           PX10 = (X>=10)*PX' % Approximate calculation
PX10 = 0.2834pX10 = cpoisson(8,10) % Direct calculation
pX10 = 0.2834M = t>=0.5*u;
PM = total(M.*P)PM = 0.1572
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The number
N of orders sent to the shipping department of a mail order house
is Poisson (700). Orders require one of seven kinds of boxes, which with packing costs havedistribution
Cost (dollars) 
0.75 
1.25 
2.00 
2.50 
3.00 
3.50 
4.00 
Probability 
0.10 
0.15 
0.15 
0.25 
0.20 
0.10 
0.05 
What is the probability the total cost of the $2.50 boxes is no greater than $475? What
is the probability the cost of the $2.50 boxes is greater than the cost of the $3.00 boxes?What is the probability the cost of the $2.50 boxes is not more than $50.00 greater than
the cost of the $3.00 boxes?
Suggestion . Truncate the Poisson distributions at about
twice the mean value.
X = 0:400;
Y = 0:300;PX = ipoisson(700*0.25,X);
PY = ipoisson(700*0.20,Y);icalc
Enter row matrix of Xvalues XEnter row matrix of Yvalues Y
Enter X probabilities PXEnter Y probabilities PY
Use array operations on matrices X, Y, PX, PY, t, u, and PP1 = (2.5*X<=475)*PX'
P1 = 0.8785M = 2.5*t<=(3*u + 50);
PM = total(M.*P)PM = 0.7500
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One car in 5 in a certain community is a Volvo. If the number of cars passing a
traffic check point in an hour is Poisson (130), what is the expected number of Volvos? Whatis the probability of at least 30 Volvos? What is the probability the number of Volvos is
between 16 and 40 (inclusive)?
P1 = cpoisson(130*0.2,30) = 0.2407
P2 = cpoisson(26,16)  cpoisson(26,41) = 0.9819
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A service center on an interstate highway experiences customers in a onehour
period as follows:
 Northbound: Total vehicles: Poisson (200). Twenty percent are trucks.
 Southbound: Total vehicles: Poisson (180). Twenty five percent are trucks.
 Each truck has one or two persons, with respective probabilities 0.7 and 0.3.
 Each car has 1, 2, 3, 4, or 5 persons, with probabilities 0.3, 0.3, 0.2, 0.1, 0.1, respectively
Under the usual independence assumptions, let
D be the number of persons to be served.
Determine
$E\left[D\right]$ ,
$\mathrm{Var}\phantom{\rule{0.166667em}{0ex}}\left[D\right]$ , and the generating function
${g}_{D}\left(s\right)$ .
$T\sim $ Poisson (200*0.2 + 180*0.25 = 85),
$P\sim $ Poisson
(200*0.8 + 180*0.75 = 295).
a = 85
b = 200*0.8 + 180*0.75b = 295
YT = [1 2];
PYT = [0.7 0.3];
EYT = dot(YT,PYT)EYT = 1.3000
VYT = dot(YT.^2,PYT)  EYT^2VYT = 0.2100
YP = 1:5;PYP = 0.1*[3 3 2 1 1];EYP = dot(YP,PYP)
EYP = 2.4000VYP = dot(YP.^2,PYP)  EYP^2
VYP = 1.6400EDT = 85*EYT
EDT = 110.5000EDP = 295*EYP
EDP = 708.0000ED = EDT + EDP
ED = 818.5000VT = 85*(VYT + EYT^2)
VT = 161.5000VP = 295*(VYP + EYP^2)
VP = 2183VD = VT + VP
VD = 2.2705e+03NT = 0:180; % Possible alternativegNT = ipoisson(85,NT);
gYT = 0.1*[0 7 3];
[DT,PDT]= gendf(gNT,gYT);
EDT = dot(DT,PDT)EDT = 110.5000
VDT = dot(DT.^2,PDT)  EDT^2VDT = 161.5000
NP = 0:500;gNP = ipoisson(295,NP);
gYP = 0.1*[0 3 2 2 1 1];
[DP,PDP]= gendf(gNP,gYP); % Requires too much memory
$${g}_{DT}\left(s\right)=exp(85(0.7s+0.3{s}^{2}1))\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{g}_{DP}\left(s\right)=exp\left(295(0.1(3s+3{s}^{2}2{s}^{3}+{s}^{4}+{s}^{5})1)\right)$$
$${g}_{D}\left(s\right)={g}_{DT}\left(s\right){g}_{DP}\left(s\right)$$
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Questions & Answers
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?
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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?
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
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
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
Source:
OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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