Continuous Random Variables
6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Forum Code Workbook ICS214 Assignment 3 Continuous Random Variables ICS214 Assignment 3 Continuous Random Variables 1. Complete all the problems below and show your work. 2. In addition to the LOs listed next to each problem, you will be graded on #MathTools, #CompTools, and #Professionalism for the overall quality of your text, math, and code. 3. You may upload a Python notebook containing all your work, a PDF with your text and math and a Python notebook with your code separately (please indicate “see code book” or “see PDF” in the text box for each problem you do that way). No handwritten submissions. Problem 1. Bus Lines (#Probability, #ParameterEstimation) Maria arrives at a bus stop at a uniformly random time. When Maria arrives at the bus stop, either of two independent bus lines (both of which can take her home) may come by. Company A’s bus arrival times are exactly 10 minutes apart, whereas the time from one 1 Company B bus to the next is distributed as Expo( ). 10 1. What is the probability that Company B’s bus arrives first? 2. What is the PDF of Maria’s waiting time for a bus? Be sure to state what the support of the distribution is. 3. Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.Question 1 of 7 1.1 What is the probability that Company B’s bus arrives first? Normal Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | Restart | Interrupt https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 1/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Code Cell 1 of 14 In [ ] 1 #USE AS NEEDED Run Code Question 2 of 7 1.2 What is the PDF of Maria’s waiting time for a bus? Be sure to state what the support of the distribution is. Normal Code Cell 2 of 14 In [ ] 1 #USE AS NEEDED Run Code Question 3 of 7 1.3 Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct. Normal Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 2/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Code Cell 3 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 4 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 5 of 14 In [ ] 1 #USE AS NEEDED Run Code Problem 2. Counting Votes (#Distributions) In a small voting district, P oisson(λ)people arrive to vote during a referendum. Each voter votes for the proposal with probability p and against the proposal with probability (1 − p). Assume everyone casts their vote independently. 1. If D is the difference between the number of votes for the proposal and the number of votes against the proposal, determine E(D) and V ar(D). 2. Implement a simulation to check your answers. Question 4 of 7 2.1 If D is the difference between the number of votes for the proposal and the number of votes against the proposal, determine E(D) and V ar(D). Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 3/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Normal Code Cell 6 of 14 In [ ] 1 #USE AS NEEDED Run Code 2.2 Implement a simulation to check your answers. Code Cell 7 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 8 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 9 of 14 In [ ] 1 #USE AS NEEDED Run Code Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 4/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Problem 3. Stick-breaking (#Probability) A stick of length 1 is broken into two pieces, at a uniformly random break point. (3.1) Find the CDF of the length of the smaller piece. (3.2) What is the average length of the smaller piece? Question 5 of 7 3.1 Find the CDF of the length of the smaller piece. Normal Code Cell 10 of 14 In [ ] 1 #USE AS NEEDED Run Code Question 6 of 7 3.2. What is the average length of the smaller piece? Normal Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 5/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Code Cell 11 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 12 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 13 of 14 In [ ] 1 #USE AS NEEDED Run Code Code Cell 14 of 14 In [ ] 1 #USE AS NEEDED Run Code Question 7 of 7 Please create a PDF, include ALL of your answers to the assignment, and submit it here. Please indicate in the text boxes above “See PDF” as appropriate. Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 6/7 6/17/24, 8:55 PM ICS214 Assignment 3 Continuous Random Variables Drop or upload a file here Python 3 (384MB RAM) | Edit Run All Cells Kernel Ready | | https://sle-collaboration.minervaproject.com/?id=d89dbaf6-83bd-4aea-a600-25de4d5fdc68&userId=24563&name=Alsayedhussain+Ali+Mohamed… 7/7
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