# 15.2 Problems on random selection  (Page 5/7)

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

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 2.5 3 3.5 4 Probability 0.1 0.15 0.15 0.25 0.2 0.1 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 X-values XEnter row matrix of Y-values 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

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

A service center on an interstate highway experiences customers in a one-hour 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
${g}_{DT}\left(s\right)=exp\left(85\left(0.7s+0.3{s}^{2}-1\right)\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{g}_{DP}\left(s\right)=exp\left(295\left(0.1\left(3s+3{s}^{2}2{s}^{3}+{s}^{4}+{s}^{5}\right)-1\right)\right)$
${g}_{D}\left(s\right)={g}_{DT}\left(s\right){g}_{DP}\left(s\right)$

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
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
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
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