Trading assistant intern Interview Questions in United States

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TransMarket Group
Trading Assistant Intern was asked...June 12, 2012

What the probability of getting 2 consecutive heads in a total of N tosses (I found this one pretty hard and I didn't figure out the right answer at the time.)

6 Answers

I think the answer should be this: Since the probability of getting two heads in a row and getting two tails in a row is the same, we only need to figure out the probability of the total. The remaining event is: 1 head 1 tail......due to different order, events should be 2 Therefore the probability=0.5(1-2(1/2)^N)=0.5(1-(1/2)^(N-1)) Less

sorry for all the typos, the solution should be understandable in spite of that.

This can be solved by considering the number of sequences of heads/tails that do NOT have consecutive heads. If N coins are tossed, you can have 0 heads in 1 way. You can have 1 head in N ways--choose 1 from any of the N positions in the sequence. You can have 2 heads as long as they are not consecutive. Imagine you have N-2 tails and you need to decide where to place the 2 heads. You can insert them before any of the tails, or after the last tail--so you need to choose 2 out of a possible N-1 positions. Similarly, for any H less than or equal to N/2, you can have H heads by selecting H positions from a possible (N-H)+1 positions. So the number of sequences which do NOT have two consecutive heads can be found by the sum: 1 + nCr(N,1) + nCr(N-1,2) + nCr(N-2,3) + ... Evaluating this starting with N = 2 gives the values 3, 5, 8, 13, 21, 34, ... These are Fibonacci numbers. The number of sequences of length N without 2 consecutive heads is given by F_{N+2}, where F_1 = 1, F_2 = 1, and F_N = F_{N-1} + F_{N-2}. It follows that the probability for obtaining two consecutive heads in N flips of a fair coin is given by 1 - ( F_{N+2}/ 2^N). Note: j-dw has a correct solution. The solution given by Charles ignores the fact that many sequences will have BOTH two consecutive tails AND consecutive heads. He treats these as non-overlapping sets. Delusion ignores all cases such as HTTHTTHTT in which there is more than one T separating the heads. Less

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Chicago Trading Company

What is 29^2?

4 Answers

Mental math. You could do it mentally. 29 is close to 30. So the upper bound is 30*30 = 900. You would have to subtract 30 and 29. 900- 59 = 841. Less

Easiest way I can think of is to mentally calculate (30-1)(30-1) and then mentally foil the answers. You end up getting 900 - 30 - 30 + 1 = 841 which is pretty easy to do in your head. Less

or, take 29 x 30 to get 870. Take away one 29, get 841. Same idea, but more elegant. You've multipled 29 thirty times, you only need 29 of them, so take one away. Less

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Belvedere Trading

If you roll a dice and and receive a dollar for whatever number you role (i.e. $1 for rolling a 1, $2 for a 2 etc.), what is the expected value of rolling this dice

1 Answers

$3.50

TransMarket Group

Given a covariance matrix, how to get the corresponding correlation matrix.

1 Answers

Just divide by the product of the standard deviations of the two variables.

Chicago Trading Company

Describe a situation where you were working with a team and had to overcome some sort of challenge.

1 Answers

You should have an answer prepared before the interview for these types of questions. Less

Monetary Authority of Singapore

asked about the stock market trend and exchange rates

Belvedere Trading

Why do you want to be a trader?

Chicago Trading Company

What's your favorite TV show; why? What's your dream job? What DON'T you like about CTC? If ___ Trading (I can't remember, maybe Spot or some other prop shop) offered you 50k more per year, would you leave; why?

TransMarket Group

Calculate the eigen value of a 2*2 matrix

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