# 5.8 Homework

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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.

 $x$ $P\left(X=x\right)$ $x\cdot P\left(X=x\right)$ 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

 $x$ $P\left(X=x\right)$ $x\cdot P\left(X=x\right)$ 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.

 $x$ $P\left(X=x\right)$ 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.
sure. what is your question?
20/(×-6^2)
Salomon
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
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
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
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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