CS544 Module 4 Assignment
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CS544 Module 4 Assignment
Use the appropriate R functions for the corresponding distributions for the following questions. For the items underlined below (Part1 b, Part2 b, Part3 b), check the answer obtained using the R function with the explicit formula calculation. Show both the solutions.
Part1) Binomial distribution (20 points)
Suppose a student has 40% chance of scoring a perfect score in an exam with
a) Compute and plot the probability distribution for the number of perfect scores over
Part2) Negative Binomial distribution (20 points)
Suppose a student has 60% chance of scoring a perfect score in an exam with
a) Compute and plot the probability distribution for scoring the three perfect scores (both
b) What is the probability that the student will have the three perfect scores with exactly
Part3) Hypergeometric distribution (20 points)
Suppose that your professor created a pool of 60 multiple choice questions and 40
a) Compute and plot the probability distribution for the number of multiple choice
Part4) Poisson distribution (20 points)
Suppose that, on an average, students email 10 questions per day to the professor.
a) What is the probability that the professor will have to answer exactly 8 questions per
b) What is the probability that the professor will have to answer at most 8 questions per
c) What is the probability that the professor will have to answer between 6 and 12
d) Calculate and plot the PMF for the first 20 questions.
professor gets per day over the course run. Show a barplot of the frequencies of the
from the plots?
Part5) Normal distribution (20 points)
Suppose that visitors at a theme park spend an average of $100 on souvenirs. Assume
a) Plot the PDF of this distribution covering the three standard deviations on either side
b) What are the chances that a randomly selected visitor will spend more than $120?
(inclusive)?
deviations, and three standard deviations, respectively?
f) If the theme park gives a free T-shirt for the top 2% of the spenders, what will be the
g) Show a plot for 10,000 visitors using the above distribution.
Submission:
When the term lastName is referenced, please replace it with your last name.
Create a folder, CS544_HW4_LastName and place the following files in this folder. Provide all R code in a single file, CS544_HW4_LastName.R. Clearly mark each subpart of each question.
Provide the corresponding outputs from the R console in a single Word document, CS544_HW4_LastName.doc.
Archive the folder (CS544_HW4_LastName.zip). Upload the zip file to the Assignments section of Blackboard.
2022-05-06