<< Chapter < Page Chapter >> Page >

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
Got questions? Get instant answers now!

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 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
Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

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 [ D ] , Var [ D ] , and the generating function g D ( s ) .

T Poisson (200*0.2 + 180*0.25 = 85), P 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 D T ( s ) = exp ( 85 ( 0 . 7 s + 0 . 3 s 2 - 1 )) g D P ( s ) = exp ( 295 ( 0 . 1 ( 3 s + 3 s 2 2 s 3 + s 4 + s 5 ) - 1 ) )
g D ( s ) = g D T ( s ) g D P ( s )
Got questions? Get instant answers now!

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive
Samson Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Applied probability' conversation and receive update notifications?