



This module provides a number of homework exercises related to Discrete Random Variables. The module is based on the original module in the textbook collection Collaborative Statistics by Susan Dean and Dr. Barbara Illowsky and has been modified. New problems (#38 to #43) have been added.
1. Complete the PDF and answer the questions.
$X$ 
$P(X=x)$ 
$X\cdot P(X=x)$ 
0 
0.3 

1 
0.2 

2 


3 
0.4 


A
Find the probability that
$X=2$ .

B
Find the expected value.
Suppose that you are offered the following “deal.” You roll a die. If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you pay $6.

A
What are you ultimately interested in here (the value of the roll or the money you win)?

B
In words, define the Random Variable
$X$ .

C
List the values that
$X$ may take on.

D
Construct a PDF.

E
Over the long run of playing this game, what are your expected average winnings per game?

F
Based on numerical values, should you take the deal? Explain your decision in complete sentences.
A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars.

A
Construct a PDF for each investment.

B
Find the expected value for each investment.

C
Which is the safest investment? Why do you think so?

D
Which is the riskiest investment? Why do you think so?

E
Which investment has the highest expected return, on average?

B
$200,000;$600,000;$400,000

C
third investment

D
first investment

E
second investment
A theater group holds a fundraiser. It sells 100 raffle tickets for $5 apiece. Suppose you purchase 4 tickets. The prize is 2 passes to a Broadway show, worth a total of $150.

A
What are you interested in here?

B
In words, define the Random Variable
$X$ .

C
List the values that
$X$ may take on.

D
Construct a PDF.

E
If this fundraiser is repeated often and you always purchase 4 tickets, what would be your expected average winnings per game?
Suppose that 20,000 married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let
$X$ = the number of children
$X$ 
$P(X=x)$ 
$X\cdot P(X=x)$ 
0 
0.10 

1 
0.20 

2 
0.30 

3 


4 
0.10 

5 
0.05 

6 (or more) 
0.05 


A
Find the probability that a married adult has 3 children.

B
In words, what does the expected value in this example represent?

C
Find the expected value.

D
Is it more likely that a married adult will have 2 – 3 children or 4 – 6 children? How do you know?

A
0.2

C
2.35

D
23 children
Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given below.
$X$ 
$P(X=x)$ 
3 
0.05 
4 
0.40 
5 
0.30 
6 
0.15 
7 
0.10 

A
In words, define the Random Variable
$X$ .

B
What does it mean that the values 0, 1, and 2 are not included for
$X$ on the PDF?

C
On average, how many years do you expect it to take for an individual to earn a B.S.?
Questions & Answers
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
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 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
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?
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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