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Discrete Random Variables: Homework is part of the collection col10555 written by Barbara Illowsky and Susan Dean Homework and provides a number of homework exercises related to Discrete Random Variables (binomial, geometric, hypergeometric and Poisson) with contributions from Roberta Bloom.

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 raffle?

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} {} in the PDF?
  • On average, how many years do you expect it to take for an individual to earn a B.S.?

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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