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# [] [ת]Columbia B-School Summer Research Program˵

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cynthiawyx 2014-5-1 02:31:26 | ʾȫ¥ |Ķģʽ

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Ҫ ¼ ſػ鿴ûʺţȡɻ,ȥinstantע!

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һƪ˺˲ϱܶε¡ȻûоɾתͬѧòʵĻ鷳һҪҰһɾȻеĹ۵㶼ͬǾûкܶϢջڴлԭߣҲңϣҶջ񡣱ӵģûԭ־ıⴿΪΪȽϺʵµһݣϣҶӡԭĵַ http://blog.renren.com/GetEntry.do?id=926567572&owner=246956121NY Jotting -- Apr 29, 2014ߣ ݻ Mr.
עĩѾеһЩȤ~

I. CV Screening (Passing Rate: 150/1000+)
CBS Summer Research Program յ1000ݼ¼ȡ19ˣ¼ȡʲ2%йpoolߣABCΪ400 ʵ˽150ӡ߼ȫԿڵϣʵй߱ﵽ˽50%г70%FinanceEconomicsҪ򡣣BTWǵյտʼǶʱͬÿһҵڳ緹ʱ໥һЩ㡱йpoolPS˵ԼСͶĳĽѾðȻֻƴˣŷߵʵϰŮѰũзΧ֮ġ

(1). ѧйȻҪռйĽ50%˵ʵ¼ȡ߸е𾪵ľֲʵGPA 3.85+ һһƬʲôΪϡ飨׹ĵGradingƶȼֱ˷ָؼǴԼ߳ɵļǡ˫רѧORͳ+OR̿˫רҵһЩðļǳ˽ӽTriple Majorϣ˫ר ټϼOR˳ѧΪרҵټһЩʵʵϰ߿оԼTop School֪8+3׹ѧԺTop5

(2). йƱmasterĿѧ߱Ŀ˵Ъ2+2ࣩ֮ͬռйĽ50%GPApoolǳΪһjoke ǵdirectorЦ˵йmasterѧֻҪλ4ͿˢȻʵûôGPAûгΪˢ˵Ĺؼأἰ

(3). һЩ⣬ĸҵѧУڶPHDѧUchicagoUpennMITPurdueڱֱѧҲи𼸸ЩϾcase-by-case checking
. 牛人云集,一亩三分地
һǿӲҪGPAԼǷ߱һĿγҪ󣨸ûڿ50%ߣ
ӵйƱˣȸѧУһRanking䣬Ȼϱ+˶ʿɼۺϿǣһ˵ҪɼȫA + ƹTopѧУ OR TopѧУTop༶ܹһءȻͬѧУGPA׼Ҳǲͬģ˵ԺֽϵUchicagoҪͻ½һЩ
ڶϸ鿴ʣCVеĹûڿʣе70%~80%ÿݲϽᱻ˿һҪ˸YesһYesʣMaybeͨһġԼԿԡܷصҪ ʱй½ߵƾͿʼֳһ棬ڵʵϰ඼ڵؿȱһЩܹŷ Ӳ(Hard-skill) ԼһֵĹݣһ棬ǱȽϿⱳĻϾмֵо󲿷ֶڹѧڼɵģһϾͱȾʱӲرȥܶ붼˿ڵƼеñʶһҪһѧʲôӡ
ɸѡйpool߶ֽϷǳǿʵֵsample
(1). Top 2 ƣIvy master Ŀ GPA 4.2+EngineeringˣһǹѧУһ(Top30Class Rank 2/200+)Ivy CS masterڼγȫA+Ҳ4.33һCSָµbiology network⣻
(2). Yale ƣTriple Major (Economic Major + CS Minor + Math Minor) GPA 3.97National Research Labortary + 1Mortgage market modellingйIntern
(3). Top10 + Top5 Master + 3깤 + Ivy mfeGPA4.0
(4). ԺRank 1st +תѧEcon major Rank 1stȷָҪоʦŷ޵pool˲˽⣩
(5). +Top 20 Bschool Master+5 Econ &STAT PHDγ̱GPA3.95
(6). stanford+Uchicago STAT PHD꼶ѧһUpenn MATH PHD꼶ƺABC
Ȼ˵й˺ǿҲзǳBTӡг˽⵽ģ
(1). Stanford ƣԤҵStuyvesant High School֪ĿԼȥһ£˫ר+Python,MATLAB,STATA,JavaGPA 4.00ѾѧһЩgrad levelγ̣Real Analysis, Time Series, Game Theory, Advanced Micro, Advanced EconometricsѾColumbia Business SchoolĽworking paperStanfordһGender ResearchĿ⣬ͬʱڿеStanford Economics Association Vice PresidentԼStanford Undergraduate Research JournalࣨBTı˹ϵRock Star˾ǰԲȡˡ
(2). Columbia ƣFinancial Engingeering Major + CS Minor + Economics Minor, GPA 4.04һͨʶB˳ɼȥſξ4.14C++,Java,STATA,Python,R,NET,MATLAB,PerlоȤ algorithm trading strategyһGoldman Sachsʵϰĸֱǣ
backtesting trading strategies (store tick data and convert into indicators for trading signal)
һִŻ㷨ڲ²гߵĽͶϵϢ
ԼһColumbia Business School йinternational stock diversificationĿ⣨ڵƼŽ롣

II. Interview (Passing Rate:40/150)
passʣ߽Իڣɰڵͬ¸ݸԲͬó䱻ԵԼд⣨ߺһͬ¸˽϶finance concentrationбҪи𲿷ֵйߣ
(1). ϴʵݱȽtricky֪ʶҪԹ̽ƫ졣һСʱʱ佫15~20Ҵ⣨ߵıֵѶȣڻشȷ30%~40%ңֵ÷֣ѧ/ͳ++finance concentrationĻ̣ÿһֳõprogramming tool׼˶Ӧ1~2Ŀ+Research-based questionsԼһЩpersonal questionsߵCVһЩ⣬δȵȣ
(2). ԹǹסĿʱһЩʣӶõһЩHints Communication skillsомҪʵ ˵ĹǣûܹʲôĿܴTA˼ǷȷĹ켣ϣԼǷܹԼתΪмֵⲢӢԽн̸̶ܴϾһʵܹЧо񣻴ĿѶҪܵͣϸϿסĻԵϲ飩ȫû˼·Ļ򽫻ԸCVϵؾɣMATLABϵͳDebug Mode˽⣬Python߰˽⣬ȵȣ
(3). Personality ԹȫҪskypeƵֱon-siteԱڹ۲챻ʱʱ巴ӦвCVֽǿʱԺĿʧȥģǴ󲿷ԹصжǱַǳ侲һ˼̬ȣ
(4). Research-Based QuestionȤĵطмֱӴԼƽʱprojectľתĿͨҪȥԼĻҪʲôĴ𰸣Լͨŵ˼άһʾ¸ȷĽֵĿҸĩȤĻԿһ£

Թб߷һЩǳ˼
Case No.1ſƷǳfancyCVԹвٱ¶صĻʵԼCVˮ̫ࡣһColumbia GPA ~3.9 Engineering + Econ Double MajorCVгԼֱѧԺ⣨һõnatrual language processingһõweb-scrapingSASȥ칫ڵõĴǸ֪ѧ˭˽⵽ǺµPHDɻҷһ㣩Ը˱б߱׼һЩйȻԴԼͳĻ⣬Էtotally lost ҾTAΪʲôЩCVгĶTAȻȫ˽⣬õĴǸֱӰRAʱдġܡֱӸճCV档
Case No.2йƱ˶ʿˣںGPAطĵĴ󻷾£ڼڹڵıֵȷܹӳ˵ʵˮƽ ͨ¹ѧУRanking30~50top 2%ѧӲʵϵȷҪڹ廪averageˮƽѧֹܻαԵpool~430ıƣ˶ʿڼGPA>= 4.0ߣʱıȫྶͥһѧ浽ֱЩĿͬѧûܹشһ±ֽϺõڹڵıרҵһ2/~200һ1/~140ʱҾ롰ѧʱƣʵĻܴ󲿷һͬѧԺΪʲômasterԿγѹͬʱҽôĿ⣬ĻشԼPHD֪ԼԺУǺӲҪֵĸɫаĿ ߾ǰᵽ GPA 4.33ȫA+ѧЩһԱֱǡ
Case No.3financeeconomicsоһԳ(1). Mathematical OR Computational Finance Լ (2) Financial EconomicsQuant FinanceֶȽģĴʣһ˵ǰѧ/ͳ+script languageشĽϺã߾ѧĿ&ͳشĽϺãȻҲ涼õġǵʵؼResearch-Based Questionʱ߱ȽϾȵFinancial EconomicsıѧԸܹҵ˼·ȻѧϲһĳMathematical OR Computational Financeѧtotally at lostֱ߸һԵʾʱŻȻԭӡ˵ĿǶڱȽϴͳfinanceҲǶһЩ˵financial engineeringmathematical financeоѵ㲻ڸһѾȥһmodelȥҵһоⱳĹؼڴ˻νԼĽģ˼ʼսҪȥ֤˼·ʹģӾѧǶ壨economically make sense
ԼԭȱҲsciencephysics׹ǰһֱѧfinanceǾ˼˺𽥾Mathematical OR Computational FinanceindustryҵϱȽһƣϾʵϣǶڶmodelling idea⣬ҪķǺܶΪȽ׵ľѧ֪ʶһ һ˵ĻѶȾԶԶڡһѧ⡱ô򵥣ѧרҵﱾƵоѶȿרҵ֮һȻЩȫǸ˵ļ⣬вͬĻ԰ҵĹ۵㵱Ц
Case No.4˳һ£Թstand outUchicago Ugrad + MasterһѧMicrosoftȫְCanyon Partnersʵϰľ飩ʱҲĳһԵ㣬EconⲻܹȫȷĴ𰸣ô˫רͲΪʲôȷҲ70%ԶԶ˵30%~40%ʱΪʲô΢ȥԼδ㣩ҵĻشlife styleҪģԼһЩfinancial researchĶȻPHDindustryûȷĴ𰸣Թû̫fancyĻش𣬵Ǳsensehard-skill϶൱ĳɫӦĽfinal pool

III. Final pool decision (Passing Rate: 19/40)
final poolн40ѧǽĿֻ19˭ܹõofferɱϼResearch DirectorԼھ
Ժȡȷ˴һ ͬ¶ԼƼҵֵı30%ߺһͬʱͬfinanceһռֻѧΧԼһпʱף˽귢ȥоĿѧreturn offer⣬ʣ17behavioral experimentĿ⾹Ȼ7ȥֻ1 һbehavioralͬƼ5~6ȫ¼ȡdirectorһЩѧȻeconomicsoperation management, marketing, accounting¶1~3ռfinanceһռ40%ңĿֻС2
directorõĴǣʵģҪǽǾҪԿڵѧʵ޷ȷЩ෽ѧڻbehavioralҲúܺãso that's it
ͷһ1000ˣ¼ȡ19¼ȡʲ2%ʱѡfinance concentration˴Թ40%ңո÷ֻ¼ȡ2ѧ Ҳfinance¼ȡʼʹֹҲֻ0.5%
һ¼ȡ̣ѧУʱյľһЩĻǿѨ磺
We've received qualified applicants far more than we can accommodate, so our final decision combines both applicant's merit as well as our faculty's research interest.

IV. Summary:
1. ׹Bschool Academic-oriented ProgramҪָPHDѧMasterԼSummer Research MBAIndustrial-oriented/˶ʿĿ㣩ѶȳֳHighly-rocketingơӱһ˵RankingȽϿǰ˵Top30BschoolЩĿ¼ȡһ2%£нһChinese Poolһ˵¼ȡѧŷޣѧԼΪ2:2:1ͬѧУһĲ𣩣й˱75%һۺйѧɹʴԼǧ֮ңڴͳȽŵFinance, Quantitative Marketingıܻ͡
. 牛人云集,一亩三分地
2. High randomnessfinanceeconomicsоһȽϹϵǣֻҪɼﵽһlevelóɼĸߵͺѧδоʵ֮ʵûֱӵĹԵġ˼·෽ѧĿУϸߵĳɼ+߱ԿڵĿγֻ̡Ϊ˹һɸѡأȻӲʵBTĻʰѧ֮ࡪۣʣɸѡ̽עڹ۲ߵʵϰ⣬оԼЩֳʵоʱƼžͳΪҪأʹˣһ߿˵ȡslot֮ıܹﵽ10:1ʱࣻһCVԼдľԼνƼŶǺܻܿкǿbiasģοкܶʵǳǿΪʱsellԼ±ȥۣ£ܶʱʵ޷ȷ˭ŸǿѧǱʱһЩءpersonal connectionso-called research matchnessȵȾͻ𵽾ãܹӳ֮ôIn my option the answer is simply: NO.

3. תеѣǰᵽComputational Finance Mathematical FinanceѧڻشһЩʱ׳ Original idea Լ Economic sense Բ⣬ܸҪǣЩ׻ᷴʱȽƫƵ߿ϡƫñӡ˿࣬һȽϴFINAECONһȽԣпܵĽѡôӡͳѧΪߵĲȷʵ̫ˡбҲΪרҵѧFinance ConcentrationҶһЩ/ڿγ̣ıComputational Finance/Mathematical FinanceӦOKFinancial EconomicsĻпضˣΪĻECONFINA˽̶ȣʵ̫ дӿֵġ˫ר+CSˣͳѧ߱ϵƽһ

4. ƣDouble MajorTriple Major+ GPA >=3.9 + 1~2summer intern/research + 1~2Կproject + ڽǿƼ -- α߼ֽϷǳ۵˵ı׼ıʵڲʲôϡ¶ ȶԣйƱѧ˵ȫλƣ
(1). ȱٶרҵĸϱ;
(2). ԺУԼγϲױȫϿɣЩʱγ̵Ӣķ붼
(3). оʵϰĺڿ͹ϲˮƽ;
(4). ӢۺҲһʺţBschoolҪ
(5). ټֵĿ͹۲أ˵CBSоĿ6³Ϳʼʱѧ׼ĩ޷ȥλᣩҪƼţμǰĵ2ܽᣩ
ô4ڹѧϰʵıйҪǿô˵һ׵Ĺǣóйɼǰ20%ǰ20%йڹרҵרҵƽڵ3030£ڵıѧںϾгԽʵ̴һͨ۲조˭ȥáȥƲ⡰˭ʵǿḶ́FinanceEconomics಻Ӳָѧ򣬱biasƣοеȷһЩμѧTop Schoolֿν绢Ȼʱ͡

5. Everything is only a starting point¼ȡ19˿͹˵ǿǵ߿project listʱ򣬾ѾʶǿĺȻǵʦȨ϶ŷǳĲ𡣻ԼȥһCBSĿʱһЩStanfordharvardͬѧڵΪԭܻaverage levelʱԼʶνġУᡱ߽Target Program̶ֻܴǸ˿ĶܹԼԶδĵͷȡԼۺʵĲϻۡ 㣬Լܹ⸡꣬Ͻ

󣬸߳ĲĿλ෹һ (עminÿشʱ)

General Questions:
1. (3 min, 1.5 min for interviewees + 1.5 min for raising questions)
Could you tell me one of the research / internship / project experiences that you're most proud of yourself? Please explain the detail of this experience, especially your original contribution in it.

2. (1 min)
Could you briefly say something about your career plan in the next 5 to 10 years?

MATH / STAT Questions:
3. (1 min + 2 min. 4 min at most)
(1). Assume there are two indepentdent, normal random variables A and B. A is with mean 2 and standard deviation 3, B is with mean 3 and standard deviation 4. What is the distribution of C=A-B?
(2). (After 1) Now A & B are still normal random variables once observed separately, BUT now they are correlated with unknown correlation level. Once again consider C=A-B. Is C now still follows normal distribution? What is the range of possible mean value? What is the range of possible variance?

4. (5~6 min)
Assume there is a stock price following STANDARD, no-drift Brownian Motion (NOTE: NOT Geometical Brownian Motion -- the model has been simplified). Assume at time 0, the initial stock price is 0.
(1). What is the probability that stock price will hit +1 first, before it hits -1? (Answer and brief explanations only)
(2). What is the probability that stock price will hit +4 first, before it hits -2? (Need explicit derivation steps)
(3). If the expected time for stock price to hit either +1 OR -2 is "k", what is the expected time for stock price to hit either +2 OR -4? (Answer and brief explanations only)
(4). (Hard) If the expected time for stock price to hit either +1 OR -2 is "k", what is the expected time for stock price to hit either +1 OR -8? (Answer and brief explanations only)

5. (3~4 min)
If I have 9 balls in a bag (3 red balls, 3 blue balls, 3 white balls). We wanna calculate the probability for getting 3 balls with red, blue,  white color each.
(1). What is the probability if each time we take one ball, record the color, and put it back (so there are still 9 balls when we make 2nd pick)?
(2). What is the probability if each time we take one ball, record the color, but NOT put it back (so there are only 8 balls remaining when we take the 2nd one)?
(3). What is the probability if each time we take one ball, record the color, but put back TWO ball with same color as you pick (so now there are 10 balls when we take the 2nd one)?

ECON/FINA Questions:
6. (Finance Concentration) (2.5min)
(1). Please briefly describe the key conceptial difference between "absolute risk aversion" and "relative risk aversion";
(2). Suppose there are two people A and B exactly same absolute risk aversion level. A has $1000 and he spent$200 on S&P 500 and $800 on T-Bill (risk-free); Now if we know B has$300 only, what is the allocation of B between S&P 500 and T-Bill (risk-free)?

7. (3min)
Now consider Manhattan as a isolated economic system. If a helicopter flies to Columbia Business School and drops a huge bag of money (which are picked away by students in Columbia Business School, as we assume naturally), is that event equivalent to simply adding taxes on all other Manhattan citizens? Please briefly explain why.

8. (2min)
(1). (Non-Finance Concentration) Please give 1 positive and 1 negative effect of economic globalization. For each effect, please give one specific example happened in our history (Those two examples must be on different events).
(2). (Finance Concentration) Considering the financial crisis event happened around 2008 as an example, could you give 1 positive and 1 negative effect of economic globalization (and each one with a specific example related with financial crisis)?

9. (1.5min)
Could you give one specific example about adverse selection (HINT: This concept is from Game Theory)

Programming Questions:
10. R (2 mins):
(1). I want to delete all the rows that have missing values (NA) in "age". How would you do this?
(2). These are questions about accessing the R documention from within R. How do you look up the "hist" function within R?. How do you do a fuzzy search for "median" (which means you are looking for a function with its name somehow like "median" but not exactly the same) from within R?

11. Python:
(1) (2min). Please mention 3 uncommon python modules/packages that you have used before, and explain under what circumstances did you use them (NOTE: "uncommon" means these packages are not originally included in python but need to be downloaded online)
(2) (2min). Now I have a string = "Welcome\to\Columbia" and I wanna write one-line code to change the string into the following: "*Welcome*\*to*\*Columbia*", how should I do that?
(3) (2min). Suppose there is an array containing 3 elements, each of them itself is an array containing 3 numbers. Suppose I want to sort these elements by their 2nd number in decending order (i.e., if originally A=[[4,5,6],[1,2,3],[7,8,9]], The result after processing should be B=[[7,8,9],[4,5,6],[1,2,3]]). How should we do that by using a one-line command?

12. MATLAB:
(1) (1.5min). Given an array "A" which contains 100 numbers, how to quickly find out the difference between the 3rd biggest element with the 3rd smallest element?
(2) (2min~3min) Debug is always important in any programming language. Suppose you have a 1000 line code to run and there comes an error as follows: "Index exceeds matrix dimensions." How can you check your code to figure out the error step by step? (HINT: Do you know anything about Debug Mode in MATLAB?)
(3) (2min~3min) We want to solve the x from following formula: Ax=b, where A is a n by k matrix and b is n by 1 array, the unknown x is k by 1 array. Mathematically, we know that we should multiply the inverse of A with b. However, in MATLAB, how do you input the formula that brings the best precision of the result of x? Explicit formula is needed for this question.
Hint: (If answer is wrong) Choose the answer among the following three: inv(A)*b, A/b, or A\b?.
(If answer is correct) What is the possible problems behind if one person use inv(A)*b and another guy use A\b?

13. STATA:
How do you only select observations where an "age" variable no less than 20? Please realize there might have missing numbers (denoted as ".") in STATA table.
How would you rename a set of variables named var1-var200 to VAR1-VAR200?
There are two columns (with many observations in it) in STATA table: First column is labeled as "GroupID" (1,2,...,10), Second column is labelled as "score". Please write a short code to tabulate the average score performance: Fist column is GroupId again, but second column is the average score of items with same GroupID.

14. Excel:
You wanna create a 9*9 multiplication table. To do this, you type in the first number series 1~9 on first row (from B1 to J1) and the second number series 1~9 on first column (from A2 to A10). How do you quickly fill in this 9*9 table, with each block shows the multiplication of number on the row and number on the column?

Research-Based Questions:
15.  (4~5 min)
Now we have millions of news articles extracted from the section "Abreast of Market" of Wall Street Journal. We want to find how these news information reflects the general market MACROECONOMIC situation. We designed a Python program to read two lists -- One called "Article exclusion list" and the other called "Article Acception List" -- And do following steps:
Step 1: For each news article, If it contains ANY unigram/bigrams in "Article exclusion list", it will be regarded only focused on specific company event but NOT on general market event, so it will be deleted from our database;
Step 2: For all articles passing step 1, we ONLY save those articles contains ANY unigram/bigrams in "Article Acception List", since we regard them indeed relecting the general market event.
Based on the research procedure above, please list 5 unigram (words) OR bigrams (two-word phrases) that should be possibly included in "Article exclusion list" or "Article Acception List" (5 words for each list). Please realize that:
(1). NO words can be used repeatedly (e.g., if you use "apple tree", you can not further use "apple pie", "apple tart" or "banana tree", "orange tree"...)
(2). NO words within similar category can be used more than once as well (e.g., If you use "apple", you cannot further use "banana", "orange", etc.)
(3). The quality of word (depending on whether it fits the purpose of our task) determines the final credit for this question.
.本文原创自1point3acres论坛
16. (Non-ECON major only)  (4~5min)
Suppose you wanna open a bakery beside Columbia University and you are working on estimating the consumption level of bread in this area. You have collected adequate amount of data from the neighborhood and now designing to do linear regression on personal bread consumption (Y) with other three variables(X_1, X_2, X_3):
Y:     Each individual's yearly spending on bread ($) X_1: Each individual's annual income level ($)
X_2: Each individual's distance to our bakery shop (miles)
X_3: Each individual's annual spending on shopping on amazon ($) The linear regression model is supposed to be Y=a*X_1+b*X_2+c*X_3+d, with a,b,c,d as coefficients. Assume the data is with high quality and we only focus on these four variables (i.e., do not consider other possible external variables). Please point out THREE crucial mistakes of this modelling process, and explain why. 17. (Finance concentration only) (8~10min): Suppose I wanna use simulation method to evaluate the price of a derivative, which is the combination of one European call option (with strike price K_1 =$10) and one European put option (with strike price K_2 = $8). For all following question, assume there is no discount rate, and investor is risk neutral. (1). (Easy) Conceptually, What is the difference between European option and American option? (2). (Easy) Given the final stock value at time of maturity as S, write the payoff function in terms of K_1, K_2 and S. Now we wanna use simulation method to evaluate the price of this derivative. Assume the remaining time to maturity is 5 years, initial stock price is 6, following a simple Brownian motion (Notice: NOT geometric Brownian motion) with drift$1 per year and volatility 0.4 per year.
(3). (Medium) Please design this simulation method to evaluate the price of this derivative. (Hint: How to establish the relationsihp between simulation result and the derivative's final price?)
(4). (Hard) Now Assume everything as same of question (3), except now at the end of year of 3, the investor has an additional chance to choose whether he sell his derivative with fixed price 8.5 (thus he/she quits the market) or keep holding his derivative and wait till the maturity date. Under this new addition condition, please use simulation method to evaluate the price of derivative. (Hint: What is the main diffucult point of this price evaluation? How we try to nail it?)
.本文原创自1point3acres论坛
18. (Non-finance concentration only) (8~10min):
(For this question, assume you always have a laptop in your hand, with any statistical software as you want.)
Suppose now I give you a weird coin: At the first flip, it will heads up/tails up with 50%-50% chance. But from now on, once it heads up on the previous flip, it will keep heads up with probability 3/5 on the next flip; Once it tails up on the previous flip, it will keep tails up with probability 4/5 on the next flip.
Now you want to figure out the 95% confidence level of the number of times the coin heads up if we flip it for 1000 times -- Here we just simply assume the # of times the coin heads up is symmetically distributed (but actually it's not, of course)
(1). (Easy) Basically, what is the definition of 95% confidence level?
(2). (Medium) Based on the assumption above, How to use simulation method to find the 95% confidence level of this problem? If you wanna use "if" function, please define the corresponding variable.
Now I take this coin back and give you another coin -- You know nothing about how weird this coin's flipping pattern is. But I want you try to use statistical method to guess the flipping pattern of this coin.
(3). (Medium) Before doing that, could you tell me what would you do to confirm this is NOT a simple fair coin ("fair coins" means every time it heads up/tails up with 50%-50% chance independently)?
(4). (Hard) Now embrace yourself with this question! Please tell me what's your methodology to figure out the filpping pattern of this coin step by step.
(HINT: Many students will first spend 1~2 minutes and figure out making statistics to get mean and standard deviation of flips, which is a good start; After that I will ask them:"Now you suspect that your interviewer just made a trick on you -- Actually this is exactly the SAME coin I gave to you for question (1) and (2)! Now going back to look that that weird coin -- Do you get any idea about what aspect you think necessary to figure out, in order to get the full picture of this coin's flipping pattern? After that, could you now disregard this specific coin and extend your methodology to a more general aspect?)

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