WorldQuant Quantitative Researcher interview questions

Given a time series, e.g. stock price, try to find an algorithm to find the subsequence that maximizes {last element - first element} of time O(n) What if we can at most hold the stock for k days?

There are N(sufficiently large) numbers that may repeat and x repeats more than N/2 times. Try to find an algorithm with time O(N) and space O(1) to find x.

Let's play a game: There are 3 white balls and 4 black balls in a black box. If you get a white ball out your payoff +1, and -1 with a black ball. You can stop anytime and repeat the game infinite times. Will you play the game?

Let's play another game: There are 100 balls, you and I pick the balls in turn, for each round you can pick 2^k balls(k=0,1,2,...). Do you have a strategy to win?

Given the daily return for past year(approximately 250 trading days) of the 500 componential stocks from S&P 500, we have 500*499/2 = 124750 correlation coefficients, What is the distribution of these coefficients? 1. Is it symmetric? 2. Is it shifting to the right or changing its shape? 3. Does it have a fatter tail than Gaussian? Why? 4. How to estimate the correlations? 5. Give me an estimate of the expectation of the correlations.

You have a large jar containing 999 fair pennies and one two-headed penny. Suppose you pick one coin out of the jar and flip it 10 times and get all heads, What is the probability that the coin you chose is the two-headed one?

Suppose we have a polynomial f(x) with real coefficients {a0,a1,...,an}of degree n unknown, we could input x and get the output f(x). 1. What is the minimum trials of input to get all coefficients? 2. What if all coefficients are integers? 3. What is all coefficients are positive integers?

Consider a bubble sort algorithm dealing with 1~100. What is the probability that after the first round of bubble, the 10th element is in the 20th address?

A,B and C choose a integer between 1 and 100 in turn to minimize the difference between the integer they choose and an unknown uniformly distributed random integer. B knows what A chooses and C knows what A,B choose. What is A's optimal strategy?