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This module provides a number of homework exercises related to Discrete Random Variables.

1. Complete the PDF and answer the questions.

x size 12{x} {} P ( X = x ) size 12{P \( X=x \) } {} x P ( X = x ) size 12{x cdot P \( X=x \) } {}
0 0.3
1 0.2
3 0.4

  • Find the probability that X = 2 size 12{X=2} {} .
  • Find the expected value.

  • 0.1
  • 1.6

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.

  • What are you ultimately interested in here (the value of the roll or the money you win)?
  • In words, define the Random Variable X size 12{X} {} .
  • List the values that X size 12{X} {} may take on.
  • Construct a PDF.
  • Over the long run of playing this game, what are your expected average winnings per game?
  • 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.

  • Construct a PDF for each investment.
  • Find the expected value for each investment.
  • Which is the safest investment? Why do you think so?
  • Which is the riskiest investment? Why do you think so?
  • Which investment has the highest expected return, on average?
  • $200,000;$600,000;$400,000
  • third investment
  • first investment
  • second investment

A theater group holds a fund-raiser. 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.

  • What are you interested in here?
  • In words, define the Random Variable X size 12{X} {} .
  • List the values that X size 12{X} {} may take on.
  • Construct a PDF.
  • If this fund-raiser 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 size 12{X} {} = the number of children

x size 12{x} {} P ( X = x ) size 12{P \( X=x \) } {} x P ( X = x ) size 12{x cdot P \( X=x \) } {}
0 0.10
1 0.20
2 0.30
4 0.10
5 0.05
6 (or more) 0.05

  • Find the probability that a married adult has 3 children.
  • In words, what does the expected value in this example represent?
  • Find the expected value.
  • Is it more likely that a married adult will have 2 – 3 children or 4 – 6 children? How do you know?
  • 0.2
  • 2.35
  • 2-3 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 size 12{x} {} P ( X = x ) size 12{P \( X=x \) } {}
3 0.05
4 0.40
5 0.30
6 0.15
7 0.10

  • In words, define the Random Variable X size 12{X} {} .
  • What does it mean that the values 0, 1, and 2 are not included for X size 12{X} {} on the PDF?
  • On average, how many years do you expect it to take for an individual to earn a B.S.?

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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