Quantitative Analyst Interview Questions | Glassdoor

# Quantitative Analyst Interview Questions

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Quantitative analyst interview questions shared by candidates

## Top Interview Questions

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### Quantitative Analyst at Jane Street was asked...

Feb 1, 2011
 3. There are 30 blue and 30 red balls and two urns. You play a game. Your opponent has the right to arrange the balls in the two urns as he pleases, without telling you what he did. You then must draw a ball from an urn of your choice. You win \$10 if you draw a blue ball, otherwise you get \$0. How much would you be willing to pay to play this game?2 AnswersI would pay less than 5\$ because the expected value of this game is 5\$Your opponent may put one red ball in a urn, 29 red balls and 30 blue ones in the other. So the probability you get a blue ball is approximately 1/4. So you should be willing to pay \$2.5.

### Quantitative Analyst at Goldman Sachs was asked...

Aug 4, 2010
 What is the expected value of tosses to get 3 heads in a row?4 Answers14can be found using markov chains and fundamental matrics matlab code A = [1/2 1/2 0; 1/6 1/2 1/3; 0 1/3 1/2]; E=[1 0 0; 0 1 0; 0 0 1]; X=(E-A)^(-1); P = [1; 1; 1]; C = X*P; PS = [1/8 3/8 3/8]; F = PS* C; display(C); display(F); so 14.5 average number of steps14，2^(n+1)-2,with n denotes number of headsShow More ResponsesDenote H as an expected number of tosses. The key is to solve an appropriate equation. First toss, if you get tails than the expected number of tosses is (H+1), since you have to start from the beginning.. If you get heads than you move to the next throw with the same logic: H=0.5*(H+1) + 0.5*(0.5(H+2)+0.5(0.5(H+3)+0.5*3)) H=14

### Quantitative Analyst at Cognizant Technology Solutions was asked...

Jan 29, 2010
 What are the independent and dependent variables in your model? What are the underlying assumptions of the model? What did your research indicate should be the expected parameter estimates for your independent variables? How long have you used SAS? What models/methodologies have you evoked through SAS?2 AnswersHi, I was browsing this website trying to find some information on an upcoming technical interview for statistical modeling when I came across your interview experience. I could be wrong but I think I know why your interview was harder then when you defended your masters theisis and why you did not get this job. I think the company that interviewed you was interested in your technique for statistical analysis and wanted to know how to do it themselves without needing to hire you. I could be very wrong but that is my analysis of your interview experience. Let me know what you think?!The questions that they asked, really do not seem that hard. You should know what your dependent and independent variables are, if you are writing that paper! And you should know the assumptions that you are making. And you should know which variable you expect to find positive or negative and significant. Sorry to sound rude, but these questions are quite reasonable. Now they should have made you feel comfortable, which they did not and in that way, they clearly were bad interviewers.

### Quantitative Analyst at Athena Capital Research was asked...

Jan 31, 2012
 X(t) follows BM. Prob of both X(T) and X(2T) larger than 0.4 Answers3/8Explanation: probability B1>0=1/2. Probability (B2-B1)>0=1/2. Probability (B2-B1)B2 is 1/4. There you get 3/8.sorry, i'm not quite sure i follow...Show More Responses3/8 is wrong. B(T) and B(2T)-B(T) is indep and normal dist. prob= prob(N1(T)>0)*prob(N2(T)>-N1(T))=integral of f(x)*F(-x) from 0 to inf,where f is the pdf of normal dist and F is the cdf of normal dist. replace F(-x)=1-F(x), you have the prob= integral x ( f(x)-f(x)*F(x)) from 0 to inf which is 1/4

### Quantitative Analyst at Morgan Stanley was asked...

Dec 11, 2010
 There is a big line of people waiting outside a theatre for buying tickets. The theatre owner comes out and announces that the first person to have a birthday same as someone standing before him in the line gets a free ticket. Where wil you stand to maximise your chance?5 AnswersPlease post some answers guysyour are at nth position, the possibility that the people before you have different birthdays is (365/365)*(364/365)*- - - -*(366-(n-1)) then the possibility that your birthday is in one of these days is n-1/365 so total probablilty is (365/365)*(364/365)*- - - -*(366-(n-1))*(n-1/365) Clearly you should stand where f(n)>f(n-1) and f(n)>f(n+1) solvedLet there are n people before you. The fact that a person's birthday is the same as yours is a Bernoulli trial with probability of success p = 1/366. Probability of exactly 1 success in n trials is f(n) = n*p*(1-p)**(n-1) (1). To maximize (1), solve df/dn = 0; n = -1 / ln(1-p) ~ 1/p = 366; f(366) = (1-1/366)^365 ~1/eShow More ResponsesFirst in the lineSecond in line

### Quantitative Analyst at Citi was asked...

Nov 9, 2012
 Burn two ropes, one needs 60 minus, another needs 30. How to get 45 minus time.2 Answersfirst burn the 60mins rope, fire it in both ends, after finish,30 minutes has past, then burn the other rope also start to burn on both ends. After finish, total time is 45minImagine 60 minute rope is divided into 60 segments. Cut off a length of 15 segments from the rope and tie it to the 30 minute one. Then both will finish burning after 45 minutes.

### Quantitative Analyst at Google was asked...

Jul 12, 2011
 Would you prefer to have new products through innovation or focus on your current main products? Please provide me some examples from your prior experiences to answer this question.2 AnswersI am aware that innovation is key to success for Google, and I have always been on the innovation side to explore the opportunities and being creative to come up with new products and solutions. However, I thought that this question might also be a tricky one, and therefore, I tried to emphasize the benefits of focusing on the current products in some situations as well. The answer is subjective and it also depends on the industry that you are involved in. In the end, I felt that the manager wasn't really satisfied with my answer.Think of BCG Matrix approach (Cash cow, dog, star, ?). In short you need both. You need to keep current projects to make money (cash cow, star), and then use the money to fund new ideas. It is a strategic question.

### Quantitative Analyst at Sentrana was asked...

Apr 17, 2012
 what is k means clustering1 Answerk-means clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.

### Quantitative Analyst at D. E. Shaw & Co. - Investment Firm was asked...

Dec 24, 2014
 Which is more: a) the number of stars in our galaxy, or b) the number of grains of sand that will fit in a 5 gallon bucket. How do you estimate both (a) and (b) using reasonable assumptions that a normal lay-person could verify/agree-with?1 Answera) # of stars in our galaxy ------------------------------------ Consider the milky way at night. First, estimate how many stars span a single dimension (say the entire radial span). Then assume that the milky way is a uniform density sphere or cube to get the total volume count of stars. There must be more than 1000 stars along a single dimension since otherwise the milky way would appear as a collection of single stars instead of a smooth blob to our naked eye (e.g. our eyes can easily pick out single pixels in a TV screen with ~1000 row/column pixels across our field of view). Therefore, suppose there are ~10k stars in a single dimension (which is needed for us to see a blurry white blob as the milky way at night). Now assuming a spherical (or even easier, a cubic) galaxy, we get something on the order of (10,000)^3 = 1e12 stars in the milky way. b) # sand grains in 5gal bucket ------------------------------------------ Get by simple ratio of volumes. V_bucket = 5gal ~ 20 L = 0.02 m^3 For sand, we know that a typical beach grain is smaller than a millimeter (AKA pebble size). We also know that sand is not microscopic -- we can see the individual bits if we hold it in our hand so it can't be on the micron size level. So assume it takes maybe 10 grains of sand lined up to span a millimeter. Therefore L_sand = 0.1mm = 1e-4m V_sand = (L_sand)^3 = 1e-12 m^3 Thus N ~ 2e10 grains of sand fit in the bucket. So there are more stars than sand given our assumptions. But it's a surprisingly close comparison (e.g. the numbers are in the same ballpark/orders of magnitude)!

### Quantitative Analyst at Bank of America was asked...

Jan 31, 2013
 Questions could be very detail in techniques, make sure you remember all projects you've been working on.1 AnswerTell them what you know
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