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hw09_masterNovember 14, 20191Homework 9: Resampling and the BootstrapReading: *EstimationPlease complete this notebook by filling in the cells provided.Before you begin, execute thefollowing cell to load the provided tests. Each time you start your server, you will need to executethis cell again to load the tests.Homework 9 is dueThursday, 11/7 at 11:59pm. You will receive an early submission bonuspoint if you turn in your final submission by Wednesday, 11/6 at 11:59pm. Start early so that youcan come to office hours if you’re stuck. Check the website for the office hours schedule. Late workwill not be accepted as per thepoliciesof this course.Directly sharing answers is not okay, but discussing problems with the course staff or with otherstudents is encouraged. Refer to the policies page to learn more about how to learn cooperatively.For all problems that you must write our explanations and sentences for, youmustprovide youranswer in the designated space. Moreover, throughout this homework and all future ones, please besure to not re-assign variables throughout the notebook! For example, if you usemax_temperaturein your answer to one question, do not reassign it later on.As usual,run the cell belowto import modules and autograder tests.[ ]:# Run this cell to set up the notebook, but please don't change it.# These lines import the Numpy and Datascience modules.importnumpyasnpfromdatascienceimport*# These lines do some fancy plotting magic.importmatplotlib%matplotlibinlineimportmatplotlib.pyplotaspltplt.style.use('fivethirtyeight')importwarningswarnings.simplefilter('ignore',FutureWarning)# These lines load the tests.fromclient.api.notebookimportNotebookok=Notebook('hw09.ok')1
_=ok.submit()1.11. PreliminariesThe British Royal Air Force wanted to know how many warplanes the Germans had (some numberN, which is aparameter), and they needed to estimate that quantity knowing only a randomsample of the planes’ serial numbers (from 1 toN). We know that the German’s warplanes arelabeled consecutively from 1 toN, soNwould be the total number of warplanes they have.We normally investigate the random variation among our estimates by simulating a sampling proce-dure from the population many times and computing estimates from each sample that we generate.In real life, if the RAF had known what the population looked like, they would have knownNandwould not have had any reason to think about random sampling. However, they didn’t know whatthe population looked like, so they couldn’t have run the simulations that we normally do.Simulating a sampling procedure many times was a useful exercise inunderstanding random vari-ationfor an estimate, but it’s not as useful as a tool for practical data analysis.Let’s flip that sampling idea on its head to make it practical.Givenjusta random sampleof serial numbers, we’ll estimateN, and then we’ll use simulation to find out howaccurate our estimate probably is, without ever looking at the whole population.Thisis an example of