# 10

Trading Assistant Intern interview questions shared by candidates

## Top Interview Questions

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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.)

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

### What is 29^2?

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

\$3.50

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

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