# 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)

Application of nanotechnology in medicine
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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
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Rafiq
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Damian
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LITNING
scanning tunneling microscope
Sahil
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Santosh
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Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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Bob
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brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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what king of growth are you checking .?
Renato
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why we need to study biomolecules, molecular biology in nanotechnology?
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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
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Loga
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Bharti
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 By Joli Julianna By Madison Christian By John Gabrieli By Jonathan Long By Madison Christian By David Bourgeois By Rylee Minllic By OpenStax By OpenStax By