School

University of Maryland, University College **We aren't endorsed by this school

Course

STAT 100

Subject

Statistics

Date

Aug 18, 2023

Pages

3

Uploaded by MegaOryx3440 on coursehero.com

STAT100 Problem Set 4: Discrete Random Variables
You need to submit a Word document or PDF for this assignment. Make sure you do the following:
1.
Upload only one file/document in ELMS for Problem Set 4
2.
Include your name in the document in the upper left-hand corner. Under your name, write
STAT 100. Write Problem Set 4 centered on the page.
3.
Number and letter your answers to the questions accordingly.
4.
Carefully read all problems and follow all instructions.
5.
Upload the assignment in ELMS before the deadline of Monday 7/31 at 11:59 PM otherwise it
is considered late. Make sure you save your document on your computer or email it to
yourself so that you keep an electronic copy.
STAT100 Problem Sets need to be completed by students in RStudio. Students should refer to the
Tutorial for Problem Set 4 as they are working on this problem set.
All Tutorials for Problem Sets can
be found in the STAT100 ELMS course under Modules.
There is no data file needed for Problem Set 4. All the necessary work can be
completed in RStudio without opening a data file.
Problem Set 4 has two questions worth 25 points. Read each question carefully and follow all
instructions.
Please follow these instructions for providing your responses:
•
For #1.a., 1.c., and 2.a., you MUST provide R code and RStudio output. In addition, you MUST
include your name in the comments for the R code for #1.a., 1.c., and 2.a.
•
For #1.b., 2.b., and 2.c., you can use RStudio but it is not required that you use RStudio.
Be
sure to
show all work in order to receive full credit.
•
For all other questions on Problem Set 4, you should type your responses directly in the
document you submit for Problem Set 4.

1.
(10 points)
X is a discrete random variable. The probability distribution for X is defined by the
following algebraic formula: P(X = x) =
(𝑥+5)
51
for x = 1, 2, 3, 4, 5, 6. Use this probability
distribution to answer the following questions.
a.
In RStudio, create a table summarizing the probability distribution for X. See the Tutorial
for Problem Set 4 for detailed instructions on how to create a table summarizing a
probability distribution defined by an algebraic function. Be sure to use the appropriate
names for each column of the table so that the table will be formatted in the familiar
way for a probability distribution table.
In the document you upload for this
assignment, for 1.a. you MUST include:
i.
the R code you used to generate the table, including comments.
IMPORTANT
INSTRUCTIONS: you MUST include your name in the comments for the R code
for #1.a.
ii.
an image of the table from the RStudio Console
b.
Verify that this is a legitimate probability distribution by checking that it meets the 2
properties of probability distributions (see the Tutorial for Problem Set 4 and previous
lecture slides).
You can use RStudio for the 2
nd
property, but it is not required that you
use RStudio. Be sure to
show all work to receive full credit.
c.
In RStudio, calculate the mean of X, using the appropriate formula for the mean of a
discrete random variable. See the Tutorial for Problem Set 5 for detailed instructions on
how to calculate the mean of a discrete random variable in RStudio.
In the document you
upload for this assignment, for 1.c. you MUST include:
i.
the R code you used to calculate the mean, including comments.
IMPORTANT
INSTRUCTIONS: you MUST include your name in the comments for the R code
for #1.c.
ii.
an image of output from the RStudio Console showing the value of the mean
d.
What is P(X
≥
4)?
Do not use RStudio for 1.d.;
you should type your responses directly in
the document you submit for Problem Set 5.
Show all work and provide your answer as a
decimal rounded to three decimal places.
e.
What is P(X < 3)?
Do not use RStudio for 1.e.;
you should type your responses directly in
the document you submit for Problem Set 5.
Show all work and provide your answer as a
decimal rounded to three decimal places.

2.
(15 points) 34% of U.S. adults have blood type A-positive. Suppose we take a random sample of
6 U.S. adults. Let X represent the number of adults (out of the sample of 6) with blood type A-
positive. This situation can be modeled with a binomial random variable X.
a.
In RStudio, create a table summarizing the probability distribution for X. See the Tutorial
for Problem Set 4 for detailed instructions on how to create a table summarizing a
probability distribution for a binomial random variable. Be sure to use the appropriate
names for each column of the table so that the table will be formatted in the familiar way
for a probability distribution table.
In the document you upload for this assignment, for
1.a. you MUST include
r:
i.
the R code you used to generate the table, including comments.
IMPORTANT
INSTRUCTIONS: you MUST include your name in the comments for the R code
for #2.a.
ii.
an image of the table from the RStudio Console
b.
Calculate the mean of this binomial random variable X, using the appropriate formula for
mean of a binomial random variable.
For 2.b., you can use RStudio but it is not required
that you use RStudio. Be sure to
show all work to receive full credit
.
c.
Calculate the standard deviation of this binomial random variable X, using the appropriate
formula for standard deviation of a binomial random variable.
For 2.c., you can use
RStudio but it is not required that you use RStudio. Be sure to
show all work to receive
full credit
.
d.
What is the probability that exactly three out of the six randomly selected adults have
blood type A-positive?
Do not use RStudio for 2.d.;
you should type your responses
directly in the document you submit for Problem Set 5.
Show all work and provide your
answer as a decimal rounded to three decimal places.
e.
What is the probability that less than three out of the six randomly selected adults have
blood type A-positive?
Do not use RStudio for 2.e.;
you should type your responses
directly in the document you submit for Problem Set 5.
Show all work and provide your
answer as a decimal rounded to three decimal places.
f.
What is the probability that more than three out of the six randomly selected adults have
blood type A-positive?
Do not use RStudio for 2.f.;
you should type your responses
directly in the document you submit for Problem Set 5.
Show all work and provide your
answer as a decimal rounded to three decimal places.
g.
What is the probability that between two and four (2, 3, or 4) of the six randomly selected
adults have blood type A-positive?
Do not use RStudio for 2.g.;
you should type your
responses directly in the document you submit for Problem Set 5.
Show all work and
provide your answer as a decimal rounded to three decimal places
.

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