# 15.2 Problems on random selection  (Page 3/7)

A game is played as follows:

1. A wheel is spun, giving one of the integers 0 through 9 on an equally likely basis.
2. A single die is thrown the number of times indicated by the result of the spin of the wheel. The number of points made is the total of the numbers turned up on the sequence ofthrows of the die.
3. A player pays sixteen dollars to play; a dollar is returned for each point made.

Let Y represent the number of points made and $X=Y-16$ be the net gain (possibly negative) of the player. Determine the maximum value of

X , $E\left[X\right]$ , $\mathrm{Var}\phantom{\rule{0.166667em}{0ex}}\left[X\right]$ , $P\left(X>0\right)$ , $P\left(X>=10\right)$ , $P\left(X>=16\right)$ .

gn = 0.1*ones(1,10); gy = (1/6)*[0 ones(1,6)]; [Y,PY]= gendf(gn,gy); [X,PX]= csort(Y-16,PY); M = max(X)M = 38 EX = dot(X,PX) % Check EX = En*Ey - 16 = 4.5*3.5EX = -0.2500 % 4.5*3.5 - 16 = -0.25 VX = dot(X.^2,PX) - EX^2VX = 114.1875 Ppos = (X>0)*PX' Ppos = 0.4667P10 = (X>=10)*PX' P10 = 0.2147P16 = (X>=16)*PX' P16 = 0.0803

Marvin calls on four customers. With probability ${p}_{1}=0.6$ he makes a sale in each case. Geraldine calls on five customers, with probability ${p}_{2}=0.5$ of a sale in each case. Customers who buy do so on an iid basis, and order an amount Y i (in dollars) with common distribution:

$Y=\left[200\phantom{\rule{0.277778em}{0ex}}220\phantom{\rule{0.277778em}{0ex}}240\phantom{\rule{0.277778em}{0ex}}260\phantom{\rule{0.277778em}{0ex}}280\phantom{\rule{0.277778em}{0ex}}300\right]\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}PY=\left[0.10\phantom{\rule{0.277778em}{0ex}}0.15\phantom{\rule{0.277778em}{0ex}}0.25\phantom{\rule{0.277778em}{0ex}}0.25\phantom{\rule{0.277778em}{0ex}}0.15\phantom{\rule{0.277778em}{0ex}}0.10\right]$

Let D 1 be the total sales for Marvin and D 2 the total sales for Geraldine. Let $D={D}_{1}+{D}_{2}$ . Determine the distribution and mean and variance for D 1 , D 2 , and D . Determine $P\left({D}_{1}\ge {D}_{2}\right)$ and $P\left(D\ge 1500\right)$ , $P\left(D\ge 1000\right)$ , and $P\left(D\ge 750\right)$ .

gnM = ibinom(4,0.6,0:4); gnG = ibinom(5,0.5,0:5);Y = 200:20:300; PY = 0.01*[10 15 25 25 15 10]; [D1,PD1]= mgdf(gnM,Y,PY); [D2,PD2]= mgdf(gnG,Y,PY); ED1 = dot(D1,PD1)ED1 = 600.0000 % Check: ED1 = EnM*EY = 2.4*250 VD1 = dot(D1.^2,PD1) - ED1^2VD1 = 6.1968e+04 ED2 = dot(D2,PD2)ED2 = 625.0000 % Check: ED2 = EnG*EY = 2.5*250 VD2 = dot(D2.^2,PD2) - ED2^2VD2 = 8.0175e+04 [D1,D2,t,u,PD1,PD2,P]= icalcf(D1,D2,PD1,PD2); Use array opertions on matrices X, Y, PX, PY, t, u, and P[D,PD] = csort(t+u,P);ED = dot(D,PD) ED = 1.2250e+03eD = ED1 + ED2 % Check: ED = ED1 + ED2 eD = 1.2250e+03 % (Continued next page)VD = dot(D.^2,PD) - ED^2VD = 1.4214e+05 vD = VD1 + VD2 % Check: VD = VD1 + VD2vD = 1.4214e+05 P1g2 = total((t>u).*P) P1g2 = 0.4612k = [1500 1000 750];PDk = zeros(1,3); for i = 1:3PDk(i) = (D>=k(i))*PD'; enddisp(PDk) 0.2556 0.7326 0.8872

A questionnaire is sent to twenty persons. The number who reply is a random number $N\sim$ binomial (20, 0.7). If each respondent has probability $p=0.8$ of favoring a certain proposition, what is the probability of ten or more favorable replies? Of fifteen or more?

gN = ibinom(20,0.7,0:20); gY = [0.2 0.8]; gendDo not forget zero coefficients for missing powers Enter gen fn COEFFICIENTS for gN gNEnter gen fn COEFFICIENTS for gY gY Results are in N, PN, Y, PY, D, PD, PMay use jcalc or jcalcf on N, D, P To view the distribution, call for gD.P10 = (D>=10)*PD' P10 = 0.7788P15 = (D>=15)*PD' P15 = 0.0660pD = ibinom(20,0.7*0.8,0:20); % Alternate: use D binomial (pp0) D = 0:20;p10 = (D>=10)*pD' p10 = 0.7788p15 = (D>=15)*pD' p15 = 0.0660

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
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive