WorldQuant Financial Data Scientist interview questions

Bob walked for 5 hours. First he followed a horizontal road, then walked up the mountain and finally returned to the starting point using same route. Bob’s speed on horizontal road was 4 km/h, up the mountain 3 km/h, and down the mountain 6 km/h. How many kilometers did Bob walk?

Triangle ABC has sides of length 45, 60, and 75. Place a point D randomly and uniformly inside the triangle. What is the expected value of the sum of perpendicular distances from point D to the triangle's three sides?

How many integers n such that n^n is a perfect square are there in range [100;400] ?

What is the maximal possible variance of a random variable taking values in the interval [0, 10]?

Assume there are three random variables X,Y,Z. All pairwise correlations are equal: corr(X,Y) = corr(X,Z) = corr(Y,Z) = r. What is the range of possible values of r?

You have three fair coins. You repetitively flip all coins together. After each round you remove the coins that show tails. What is the expected number of rounds until you have no coins left to flip?

Two tubes (infinite right circular cylinders) A and B of equal radii 3 cross at the angle 90 degrees (i.e. their axial lines cross at that angle). What is the volume of the intersection of A and B?