Research Summer Intern Interview Questions | Glassdoor

# Research Summer Intern Interview Questions

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Research summer intern interview questions shared by candidates

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Apr 17, 2011

### Quantitative Researcher Summer Intern at Jane Street was asked...

Apr 17, 2011
 2) A. 10 ropes, each one has one red end and one blue end. Each time, take out a red and a blue end, make them together. Repeat 10 times. The expectation of the number of loops. B. 10 ropes, no color. All the other remains the same.7 Answers1/10 + 1/9 +...+ 1 ? B is similar..1/19+1/17+etc in BE[n] = 1/n + (n-1)/n*E[n-1] = 1/n + E[n-1] For the case of n=10, you would sum up all of the numbers from 1 to 10: 1/10+1/9+ 1/8 + 1/7 ... + 1/2Show More Responsesadd an extra 1 to the previous answerFor part A), the answer is 1+1/2+1/3+...+1/10. For part B), the answer is 1+1/3+1/5+...+1/19. Explanations: For part A), ctofmtcristo has the right approach but with a typo in the equation for E[n]. To obtain the expected number of loops, we note that the first red has a 1/n chance of connecting with its opposite blue end (and forming a loop) and a (n-1)/n chance of connecting with a different rope's blue end (and not yet forming a loop), so E[n] = 1/n*(1+E[n-1]) + (n-1)/n*E[n-1] = 1/n + E[n-1], with base case E[1]=1. Then, by induction, we get E[n] = 1+1/2+1/3+...+1/n. Part B) is similar. We note that the first end now has 2n-1 possible ends to connect to, of which 1 of them is its opposite end and 2n-2 of them belong to a different rope. Then, E[n] = 1/(2n-1)*(1+E[n-1]) + (2n-2)/(2n-1)*E[n-1] = 1/(2n-1) + E[n-1], with base case E(1)=1. By induction, E[n] = 1+1/3+1/5+...+1/(2n-1).Ed's anwser is not right. Just check for the case of 3 pairs. So total cases is 3!=6. 1 case with 3 loops, 2 cases with all wrongly attached, and 3 cases with 1 loop. so expected value is (3/6)*(1) + (1/6)*(3) = 6/6 = 1... and Eds anwser gives 1+1/2 +1/3 = 11/6, which is wrong clearly.Timi, you are missing the fact that if they are "all wrongly attached" then they form a loop. Similarly, the case you are thinking of "with 1 loop" actually has 2 loops. The correct answer is still 11/6.

### Quantitative Researcher Summer Intern at Jane Street was asked...

Apr 17, 2011
 1) Tow coins, P(head)=1/3, P(tail)=2/3, design a way to get the effect of fair coin5 AnswersI guess Play 2 games , TH or HT = outcome 1, TT = outcome 2 . Both of probability 4/9 disregard HHmanipulate payouts. P(Tails) = 2/3, so if it lands on tails I get \$1. P(Heads) = 1/3, so if it lands on heads you get \$2. 2/3 * 1 = 1/3 * 2We need unbiased decision out of a biased coin. Throw the coin twice. Classify it as "heads" if we get HT and "tails" if we get TH. Disregard the other two occurrences i.e. HH and TT.Show More Responsesit's like you need to give heads another 'chance' (to double it's probability to match tails) if you get a tail, stop if you get a head, roll again and take the second resultSwift and anon are both correct, but Swift's solution is twice as efficient because 8/9 of the time, Swift only requires 2 flips, while 4/9 of the time, anon requires only two flips. Indeed, for Swift, we can show that the expected number of flips is 2.25, while for anon, the expected number of flips is double that, 4.5. Let X be the expected number of flips. Then, for Swift, EX = 2 + 1/9*EX ==> EX = 18/8 = 2.25, while for anon, EX = 2 + 5/9*EX ==> EX = 18/4=4.5.

### Summer Research Intern at Spencer Stuart was asked...

Feb 10, 2014
 Are you more of a city person or more of a suburb/country person?1 AnswerCity, definitely.

### Research Summer Intern at Egon Zehnder was asked...

Jan 24, 2013
 all basic resume questionsBe the first to answer this question

### Summer Research Intern at MIT Lincoln Laboratory was asked...

Mar 21, 2014
 How can you relate your current research to your interest and previous research. (I did research in different areas) Be the first to answer this question

### Summer Research Intern at Glenmede was asked...

Sep 9, 2013
 No unexpected questions, very fit-focused, relaxed, and intellectual. No brain teasers.Be the first to answer this question

### Summer Research Intern at IBM was asked...

Feb 9, 2011
 Some detail about technique questions, such as HL7.Be the first to answer this question

### Summer Research Intern at Dow AgroSciences was asked...

Mar 3, 2013
 How can I decrease the uncertainty of water quality modeling work with limited inputs?Be the first to answer this question

### Summer Research Intern at University of Chicago was asked...

Nov 15, 2013
 Just general inquires about my interest and skills for the position. Technical questions about MATLAB and Excel experience.Be the first to answer this question
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