# 15.2 Problems on random selection  (Page 8/7)

(See Exercise 3 from "Problems on Random Variables and Joint Distributions") A die is rolled. Let X be the number of spots that turn up. A coin is flipped X times. Let Y be the number of heads that turn up. Determine the distribution for Y .

PX = [0 (1/6)*ones(1,6)];PY = [0.5 0.5];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PX Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD) % Compare with P8-30 0.1641 1.0000 0.31252.0000 0.2578 3.0000 0.16674.0000 0.0755 5.0000 0.02086.0000 0.0026

(See Exercise 4 from "Problems on Random Variables and Joint Distributions") As a variation of [link] , suppose a pair of dice is rolled instead of a single die. Determine the distribution for Y .

PN = (1/36)*[0 0 1 2 3 4 5 6 5 4 3 2 1];PY = [0.5 0.5];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PN Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD)0 0.0269 1.0000 0.10252.0000 0.1823 3.0000 0.21584.0000 0.1954 5.0000 0.14006.0000 0.0806 7.0000 0.03758.0000 0.0140 % (Continued next page) 9.0000 0.004010.0000 0.0008 11.0000 0.000112.0000 0.0000

(See Exercise 5 from "Problems on Random Variables and Joint Distributions") Suppose a pair of dice is rolled. Let X be the total number of spots which turn up. Roll the pair an additional X times. Let Y be the number of sevens that are thrown on the X rolls. Determine the distribution for Y . What is the probability of three or more sevens?

PX = (1/36)*[0 0 1 2 3 4 5 6 5 4 3 2 1];PY = [5/6 1/6];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PX Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD)0 0.3072 1.0000 0.36602.0000 0.2152 3.0000 0.08284.0000 0.0230 5.0000 0.00486.0000 0.0008 7.0000 0.00018.0000 0.0000 9.0000 0.000010.0000 0.0000 11.0000 0.000012.0000 0.0000 P = (D>=3)*PD' P = 0.1116

(See Example 7 from "Conditional Expectation, Regression") A number X is chosen by a random selection from the integers 1 through 20 (say by drawing a card from a box). A pair of dice is thrown X times. Let Y be the number of “matches” (i.e., both ones, both twos, etc.). Determine the distribution for Y .

gN = (1/20)*[0 ones(1,20)];gY = [5/6 1/6];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN gN Enter gen fn COEFFICIENTS for gY gYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD.disp(gD)0 0.2435 1.0000 0.26612.0000 0.2113 3.0000 0.14194.0000 0.0795 5.0000 0.03706.0000 0.0144 7.0000 0.00478.0000 0.0013 9.0000 0.000310.0000 0.0001 11.0000 0.000012.0000 0.0000 13.0000 0.000014.0000 0.0000 15.0000 0.000016.0000 0.0000 17.0000 0.000018.0000 0.0000 19.0000 0.000020.0000 0.0000

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
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
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive