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A property is offered for sale. Experience indicates the number N of bids is a random variable having values 0 through 8, with respective probabilities

Number 0 1 2 3 4 5 6 7 8
Probability 0.05 0.15 0.15 0.20 0.15 0.10 0.10 0.05 0.05

The market is such that bids (in thousands of dollars) are iid symmetric triangular on [150 250].Determine the probability of at least one bid of $210,000 or more.

gN = 0.01*[5 15 15 20 15 10 10 5 5];PY = 0.5 + 0.5*(1 - (4/5)^2) PY = 0.6800>>PW = 1 - polyval(fliplr(gN),PY) PW = 0.6536%alternate gY = [0.68 0.32]; [D,PD]= gendf(gN,gY); P = (D>0)*PD' P = 0.6536
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Suppose N binomial ( 10 , 0 . 3 ) and the Y i are iid, uniform on [ 10 , 20 ] . Let V be the minimum of the N values of the Y i . Determine P ( V > t ) for integer values from 10 to 20.

gN = ibinom(10,0.3,0:10); t = 10:20;p = 0.1*(20 - t); P = polyval(fliplr(gN),p) - 0.7^10P = Columns 1 through 70.9718 0.7092 0.5104 0.3612 0.2503 0.1686 0.1092 Columns 8 through 110.0664 0.0360 0.0147 0 Pa = (0.7 + 0.3*p).^10 - 0.7^10 % Alternate form of gNPa = Columns 1 through 70.9718 0.7092 0.5104 0.3612 0.2503 0.1686 0.1092 Columns 8 through 110.0664 0.0360 0.0147 0
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Suppose a teacher is equally likely to have 0, 1, 2, 3 or 4 students come in during office hours on a given day. If the lengths of the individual visits, in minutes, areiid exponential (0.1), what is the probability that no visit will last more than 20 minutes.

gN = 0.2*ones(1,5); p = 1 - exp(-2);FW = polyval(fliplr(gN),p) FW = 0.7635gY = [p 1-p]; % Alternate[D,PD] = gendf(gN,gY);PW = (D==0)*PD' PW = 0.7635
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Twelve solid-state modules are installed in a control system. If the modules are not defective, they have practically unlimited life. However, with probability p = 0 . 05 any unit could have a defect which results in a lifetime (in hours) exponential (0.0025). Under the usual independence assumptions, what is the probability the unit does not failbecause of a defective module in the first 500 hours after installation?

p = 1 - exp(-0.0025*500); FW = (0.95 + 0.05*p)^12FW = 0.8410 gN = ibinom(12,0.05,0:12);gY = [p 1-p];[D,PD] = gendf(gN,gY);PW = (D==0)*PD' PW = 0.8410
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The number N of bids on a painting is binomial ( 10 , 0 . 3 ) . The bid amounts (in thousands of dollars) Y i form an iid class, with common density function f Y ( t ) = 0 . 005 ( 37 - 2 t ) 2 t 10 . What is the probability that the maximum amount bid is greater than $5,000?

P ( Y 5 ) = 0 . 005 2 5 ( 37 - 2 t ) d t = 0 . 45
p = 0.45; P = 1 - (0.7 + 0.3*p)^10P = 0.8352 gN = ibinom(10,0.3,0:10);gY = [p 1-p];[D,PD] = gendf(gN,gY); % D is number of "successes"Pa = (D>0)*PD' Pa = 0.8352
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A computer store offers each customer who makes a purchase of $500 or more a free chance at a drawing for a prize. The probability of winning on a draw is 0.05.Suppose the times, in hours, between sales qualifying for a drawing is exponential (4). Under the usual independence assumptions, what is the expected time between a winning draw?What is the probability of three or more winners in a ten hour day? Of five or more?

N t Poisson ( λ t ) , N D t Poisson ( λ p t ) , W D t exponential ( λ p ) .

p = 0.05; t = 10;lambda = 4; EW = 1/(lambda*p)EW = 5 PND10 = cpoisson(lambda*p*t,[3 5]) PND10 = 0.3233 0.0527
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Noise pulses arrrive on a data phone line according to an arrival process such that for each t > 0 the number N t of arrivals in time interval ( 0 , t ] , in hours, is Poisson ( 7 t ) . The i th pulse has an “intensity” Y i such that the class { Y i : 1 i } is iid, with the common distribution function F Y ( u ) = 1 - e - 2 u 2 for u 0 . Determine the probability that in an eight-hour day the intensity will not exceed two.

N 8 is Poisson (7*8 = 56) g N ( s ) = e 56 ( s - 1 ) .

t = 2; FW2 = exp(56*(1 - exp(-t^2) - 1))FW2 = 0.3586
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The number N of noise bursts on a data transmission line in a period ( 0 , t ] is Poisson ( μ t ) . The number of digit errors caused by the i th burst is Y i , with the class { Y i : 1 i } iid, Y i - 1 geometric ( p ) . An error correcting system is capable or correcting five or fewer errors in any burst. Suppose μ = 12 and p = 0 . 35 . What is the probability of no uncorrected error in two hours of operation?

F W ( k ) = g N [ P ( Y k ) ] P ( Y k ) - 1 - q k - 1 N t Poisson ( 12 t )

q = 1 - 0.35; k = 5;t = 2; mu = 12;FW = exp(mu*t*(1 - q^(k-1) - 1)) FW = 0.0138
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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
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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
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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
Smarajit Reply
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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
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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