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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 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
2
3 0.4

  • A

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

    Find the expected value.

  • A

    0.1
  • B

    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.

  • 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 size 12{X} {} .
  • C

    List the values that X size 12{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 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.

  • A

    What are you interested in here?
  • B

    In words, define the Random Variable X size 12{X} {} .
  • C

    List the values that X size 12{X} {} may take on.
  • D

    Construct a PDF.
  • E

    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
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

    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

  • A

    In words, define the Random Variable X size 12{X} {} .
  • B

    What does it mean that the values 0, 1, and 2 are not included for X size 12{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

what is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
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
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
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
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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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