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Statistical Methods for Data Science

DATA7202

Semester 1, 2021

Assignment 4 (Weight: 25%)

        Please answer the questions below. For theoretical questions, you should present rigorous proofs and appropriate explanations. Your report should be visually appealing and all questions should be answered in the order of their appearance. For programming questions, you should present your analysis of data using Python, Matlab, or R, as a short report, clearly answering the objectives and justifying the modeling (and hence statistical analysis) choices you make, as well as discussing your conclusions. Do not include excessive amounts of output in your reports. All the code should be copied into the appendix and the sources should be packaged separately and submitted on the blackboard in a zipped folder with the name:

"student_last_name.student_first_name.student_id.zip".

        For example, suppose that the student name is John Smith and the student ID is 123456789. Then, the zipped file name will be John.Smith.123456789.zip.

1. [100 Marks (see details below)] Air Secure wishes to open a number of new service desks, guaranteeing that in the long run 90% of their customers do not have to wait longer than 8 minutes in a waiting queue before they are served. Preliminary research by Air Secure showed that on arrival customers always choose the smallest queue and remain there until served. This research also investigated the passengers inter-arrival time (in minutes) and the service time. The results are summarized in data.csv. The data for the first four passengers are provided below.

inter_arrival_time service_time

1.32689531655087 4.47364233325769

0.190173284276185 3.59214966621201

0.101620716736811 4.5189272687414

0.114430104248874 9.97999506103284

Perform a Discrete-Event Simulation study in Matlab, Python, or R, to answer the following question.

How many service desks should be minimally available to meet the service re-quirements? Namely, how many service desks should be available such that in the long run 90% of their customers do not have to wait longer than 8 minutes in a waiting queue before they are served. Specifically, run the simulation for T = 3000 units of time. Discard the first 30% of the samples and use N = 50 batches to estimate the probability that a customer waits less than 8 minutes before entering the service.

Perform a Discrete-Event Simulation study to answer the following question.

(a) [15 Marks] Give the problem summary and describe the project objective.

(b) [15 Marks] Give a specification of variables used in the simulation study. In addition, show a diagram that describes the project dynamics.

(c) [40 Marks] Results and Analysis. Using tables and figures, present a clear outcome of your study. Present the corresponding confidence intervals.

(d) [20 Marks] Formulate your conclusions.

(e) [10 Marks] Appendix. Include all code files used. Explain their interaction and provide a clear and well-commented code.