# 7.2 Problems on distribution and density functions

(See Exercises 3 and 4 from "Problems on Random Variables and Probabilities"). The class $\left\{{C}_{j}:1\le j\le 10\right\}$ is a partition. Random variable X has values $\left\{1,3,2,3,4,2,1,3,5,2\right\}$ on C 1 through C 10 , respectively, with probabilities 0.08, 0.13, 0.06, 0.09, 0.14, 0.11, 0.12, 0.07, 0.11, 0.09.Determine and plot the distribution function F X .

T = [1 3 2 3 4 2 1 3 5 2];pc = 0.01*[8 13 6 9 14 11 12 7 11 9];[X,PX] = csort(T,pc);ddbn Enter row matrix of VALUES XEnter row matrix of PROBABILITIES PX % See MATLAB plot

(See Exercise 6 from "Problems on Random Variables and Probabilities"). A store has eight items for sale. The prices are $3.50,$5.00, $3.50,$7.50, $5.00,$5.00, $3.50, and$7.50, respectively.A customer comes in. She purchases one of the items with probabilities 0.10, 0.15, 0.15, 0.20, 0.10 0.05, 0.10 0.15. Therandom variable expressing the amount of her purchase may be written

$X=3.5{I}_{{C}_{1}}+5.0{I}_{{C}_{2}}+3.5{I}_{{C}_{3}}+7.5{I}_{{C}_{4}}+5.0{I}_{{C}_{5}}+5.0{I}_{{C}_{6}}+3.5{I}_{{C}_{7}}+7.5{I}_{{C}_{8}}$

Determine and plot the distribution function for X .

T = [3.5 5 3.5 7.5 5 5 3.5 7.5];pc = 0.01*[10 15 15 20 10 5 10 15];[X,PX] = csort(T,pc);ddbn Enter row matrix of VALUES XEnter row matrix of PROBABILITIES PX % See MATLAB plot

(See Exercise 12 from "Problems on Random Variables and Probabilities"). The class $\left\{A,\phantom{\rule{0.166667em}{0ex}}B,\phantom{\rule{0.166667em}{0ex}}C,\phantom{\rule{0.166667em}{0ex}}D\right\}$ has minterm probabilities

$pm=0.001*\left[5\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}7\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}6\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}8\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}9\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}14\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}22\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}33\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}21\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}32\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}50\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}75\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}86\phantom{\rule{0.277778em}{0ex}}129\phantom{\rule{0.277778em}{0ex}}201\phantom{\rule{0.277778em}{0ex}}302\right]$

Determine and plot the distribution function for the random variable $X={I}_{A}+{I}_{B}+{I}_{C}+{I}_{D}$ , which counts the number of the events which occur on a trial.

 npr06_12 Minterm probabilities in pm, coefficients in c T = sum(mintable(4)); % Alternate solution. See Exercise 12 from "Problems on Random Variables and Probabilities" [X,PX]= csort(T,pm); ddbnEnter row matrix of VALUES X Enter row matrix of PROBABILITIES PX % See MATLAB plot

Suppose a is a ten digit number. A wheel turns up the digits 0 through 9 with equal probability on each spin. On ten spins what is the probabilityof matching, in order, k or more of the ten digits in a , $0\le k\le 10$ ? Assume the initial digit may be zero.

$P=\mathtt{c}\mathtt{b}\mathtt{i}\mathtt{n}\mathtt{o}\mathtt{m}\left(10,0.1,0:10\right)$ .

In a thunderstorm in a national park there are 127 lightning strikes. Experience shows that the probability of of a lightning strike starting a fire is about0.0083. What is the probability that k fires are started, $k=0,1,2,3$ ?

P = ibinom(127,0.0083,0:3) P = 0.3470 0.3688 0.1945 0.0678

A manufacturing plant has 350 special lamps on its production lines. On any day, each lamp could fail with probability $p=0.0017$ . These lamps are critical, and must be replaced as quickly as possible. It takes about one hour toreplace a lamp, once it has failed. What is the probability that on any day the loss of production time due to lamp failaures is k or fewer hours, $k=0,\phantom{\rule{0.277778em}{0ex}}1,\phantom{\rule{0.277778em}{0ex}}2,\phantom{\rule{0.277778em}{0ex}}3,\phantom{\rule{0.277778em}{0ex}}4,\phantom{\rule{0.277778em}{0ex}}5\text{?}$

P = 1 - cbinom(350,0.0017,1:6)

= 0.5513 0.8799 0.9775 0.9968 0.9996 1.0000

Two hundred persons buy tickets for a drawing. Each ticket has probability 0.008 of winning. What is the probability of k or fewer winners, $k=2,\phantom{\rule{0.166667em}{0ex}}3,\phantom{\rule{0.166667em}{0ex}}4\text{?}$

P = 1 - cbinom(200,0.008,3:5) = 0.7838 0.9220 0.9768

Two coins are flipped twenty times. What is the probability the results match (both heads or both tails) k times, $0\le k\le 20$ ?

P = ibinom(20,1/2,0:20)

#### Questions & Answers

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
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
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
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absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
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Anassong
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Lily
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there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
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
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