Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

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.

a) Compute and plot the probability distribution for the number of multiple choice questions out of the 20 questions that the student will be given?

b) What is the probability that the student will have exactly 10 multiple choice questions out of the 20 questions in the exam?

c) What is the probability that the student will have at least 10 multiple choice questions out of the 20 questions in the exam?

d) Simulate the number of multiple choice questions for 1000 students. Show the barplot of the frequencies of the multiple-choice questions.

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 day?

b) What is the probability that the professor will have to answer at most 8 questions per day?

c) What is the probability that the professor will have to answer between 6 and 12 questions (inclusive)?

d) Calculate and plot the PMF for the first 20 questions.

e) Suppose the course runs for 50 days. Simulate the number of questions the professor gets per day over the course run. Show a barplot of the frequencies of the number of questions. Show a boxplot of the number of questions. What do you infer from the plots?

Part5) Normal distribution (20 points)

Suppose that visitors at a theme park spend an average of $100 on souvenirs. Assume that the money spent is normally distributed with a standard deviation of $10.

a) Plot the PDF of this distribution covering the three standard deviations on either side of the mean.

b) What are the chances that a randomly selected visitor will spend more than $120?

c) What is the chance that a randomly selected visitor will spend between $80 and $90 (inclusive)?

d) What are the chances of spending within one standard deviation, two standard deviations, and three standard deviations, respectively?

e) Between what two values will the middle 80% of the money spent will fall?

f) If the theme park gives a free T-shirt for the top 2% of the spenders, what will be the minimum amount you have to spend to get the free T-shirt?

g) Show a plot for 10,000 visitors using the above distribution.

Extra Credit questions (20 points)

E1) (10 points) The number of hours that a student spends on CS544 assignment is a random variable X with c.d.f.

a) Determine whether X is a discrete, continuous, or mixed variable.

b) Find P(X = 2), P(X < 2), P(X > 2), P(1 ≤ X ≤ 3), and P(X > 2 | X > 0).

c) Find E[X].

E2) (10 points) Suppose that in order for the defendant to be convicted in a jury trial, at least eight of the 12 jurors must enter a guilty vote. Assume each juror makes the correct decision with probability 0.7 independently of other jurors. If 40% of the defendants in such jury trials are innocent, what is the proportion of correct verdicts?

Submission:

When the term lastName is referenced, please replace it with your last name.

Create a folder, CS544_HW4_LastName_Last4DigitsBUID and place the following files in this folder.

Provide all R code in a single file, CS544_HW4_LastName_Last4DigitsBUID.R. Clearly mark each subpart of each question.

Provide the corresponding outputs from the R console in a single Word document,

CS544_HW4_LastName_Last4DigitsBUID.doc.

Archive the folder (CS544_HW4_LastName_Last4DigitsBUID.zip). Upload the zip file to the Assignments section of Blackboard.