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.
$x$
$P(X=x)$
$x\cdot P(X=x)$
0
0.3
1
0.2
2
3
0.4
Find the probability that
$x=2$ .
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
$X$ .
List the values that
$X$ 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
$X$ .
List the values that
$X$ 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
$X$ = 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
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.
$x$
$P(X=x)$
3
0.05
4
0.40
5
0.30
6
0.15
7
0.10
In words, define the Random Variable
$X$ .
What does it mean that the values 0, 1, and 2 are not included for
$x$ 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.
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
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.