lab 3 hot hands.pdf - Hot Hand Lab Questions 1 About 43.6...

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Unformatted text preview: Hot​ ​Hand​ ​Lab​ ​Questions 1. About​ ​43.6%​ ​of​ ​Kobe’s​ ​attempted​ ​baskets​ ​are​ ​successful. 2. Kobe’s​ ​typical​ ​streak​ ​length​ ​is​ ​0.​ ​The​ ​variability​ ​in​ ​the​ ​streak​ ​length​ ​can​ ​be​ ​described with​ ​the​ ​range,​ ​which​ ​is​ ​4,​ ​or​ ​the​ ​IQR,​ ​which​ ​is​ ​1.​ ​The​ ​shape​ ​of​ ​this​ ​distribution​ ​is right-skewed. 3. To​ ​perform​ ​this​ ​simulation,​ ​we​ ​should​ ​draw​ ​out​ ​the​ ​slips​ ​with​ ​replacement,​ ​otherwise​ ​the success​ ​probability​ ​will​ ​be​ ​different​ ​each​ ​time.​ ​For​ ​example,​ ​if​ ​we​ ​have​ ​50​ ​slips​ ​that​ ​say “hit”​ ​and​ ​50​ ​slips​ ​that​ ​say​ ​“miss”,​ ​the​ ​success​ ​probability​ ​is​ ​50%.​ ​However,​ ​if​ ​we​ ​draw out​ ​a​ ​“hit”​ ​slip​ ​without​ ​replacing​ ​it,​ ​the​ ​success​ ​probability​ ​for​ ​the​ ​next​ ​draw​ ​becomes 49.49%.​ ​Our​ ​goal​ ​is​ ​to​ ​ensure​ ​that​ ​each​ ​shot​ ​is​ ​independent​ ​of​ ​the​ ​next,​ ​therefore,​ ​the success​ ​probability​ ​should​ ​always​ ​be​ ​the​ ​same. 4. The​ ​collection​ ​now​ ​contains​ ​44​ ​hits. 5. The​ ​computer​ ​performs​ ​this​ ​simulation​ ​by​ ​randoming​ ​selecting​ ​an​ ​observation​ ​from​ ​the Sample​ ​of​ ​Hot​ ​Hand​ ​collection​ ​and​ ​recording​ ​the​ ​number​ ​of​ ​streaks.​ ​The​ ​program replaces​ ​the​ ​observation​ ​each​ ​time​ ​to​ ​make​ ​sure​ ​the​ ​probability​ ​stays​ ​the​ ​same. 6. For​ ​the​ ​simulation​ ​distribution,​ ​the​ ​typical​ ​streak​ ​length​ ​is​ ​1.​ ​The​ ​variability​ ​in​ ​the​ ​streak length​ ​can​ ​be​ ​described​ ​with​ ​the​ ​range,​ ​which​ ​is​ ​5,​ ​or​ ​the​ ​IQR,​ ​which​ ​is​ ​1.​ ​The​ ​shape​ ​of this​ ​distribution​ ​is​ ​also​ ​right-skewed. 7. Both​ ​graphs​ ​have​ ​right-skewed​ ​distribution​ ​with​ ​mode​ ​at​ ​0.​ ​The​ ​median​ ​for​ ​Kobe’s​ ​graph is​ ​0,​ ​while​ ​the​ ​median​ ​for​ ​the​ ​simulation​ ​is​ ​1.​ ​The​ ​maximum​ ​for​ ​Kobe’s​ ​graph​ ​is​ ​4,​ ​while the​ ​maximum​ ​for​ ​the​ ​simulation​ ​is​ ​5.​ ​The​ ​IQR​ ​for​ ​both​ ​distribution​ ​is​ ​1. 8. No.​ ​The​ ​simulation​ ​shows​ ​that​ ​hot​ ​hand​ ​phenomenon​ ​does​ ​not​ ​exist,​ ​and​ ​each​ ​attempted basket​ ​is​ ​independent​ ​from​ ​the​ ​next​ ​one.​ ​We​ ​come​ ​to​ ​this​ ​conclusion​ ​because​ ​the simulation​ ​assumes​ ​the​ ​player​ ​does​ ​not​ ​have​ ​hot​ ​hand,​ ​and​ ​it​ ​is​ ​fairly​ ​similar​ ​to​ ​Kobe’s distribution.​ ​It​ ​has​ ​even​ ​higher​ ​mean,​ ​median,​ ​and​ ​maximum​ ​value,​ ​therefore,​ ​we conclude​ ​that​ ​Kobe’s​ ​performance​ ​during​ ​these​ ​5​ ​games​ ​was​ ​normal​ ​to​ ​his​ ​success probability. Summary​ ​Question This​ ​lab​ ​covers​ ​many​ ​concepts​ ​from​ ​chapter​ ​5,​ ​including:​ ​randomness,​ ​probability,​ ​trial, simulation​ ​and​ ​independence.​ ​There​ ​are​ ​also​ ​concepts​ ​from​ ​the​ ​previous​ ​chapters,​ ​such​ ​as center,​ ​spread​ ​and​ ​shape​ ​of​ ​distributions.​ ​However,​ ​the​ ​textbook​ ​does​ ​not​ ​cover​ ​how replacement​ ​will​ ​change​ ​the​ ​probability.​ ​We​ ​reviewed​ ​these​ ​concepts​ ​in​ ​discussion section​ ​in​ ​preparation​ ​for​ ​the​ ​midterm​ ​exam​ ​and​ ​after​ ​the​ ​midterm​ ​exam.​ ​They​ ​also appeared​ ​in​ ​practice​ ​problems. ...
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