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.
0
0.3
1
0.2
2
3
0.4
Find the probability that
.
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
.
List the values that
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
.
List the values that
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
= the number of children
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.
3
0.05
4
0.40
5
0.30
6
0.15
7
0.10
In words, define the Random Variable
.
What does it mean that the values 0, 1, and 2 are not included for
in the PDF?
On average, how many years do you expect it to take for an individual to earn a B.S.?
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
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Source:
OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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