Trading Intern

Some guy from DE Shaw gave a talk for the math and physics clubs at my uni, encouraged us all to apply. So I did: I got an email pretty soon asking to set up an interview. Interviewer was pretty hardcore, apparently he had done a postdoc in algebraic geometry before jumping ship to join. He knew my analysis professor and asked what he was up to these days. Then straight into the interview. I got demolished by the questions. They weren't that hard, but you just had to answer on the fly. Told me not to leak online but here we go anyways...

1. My wallet has 2 nickels and 10 times. The coins are to be drawn out 1-by-1 and I'm to receive all the dimes that are drawn between the 2 nickels. What's the expectation?

2. I drop a circle of radius r on a floor tiled with parallelograms with vertical perpendicular to sides distance x, horizontal perpendicular to sides distance y. What's the probability the circle lands completely within a parallelogram?

3. Randomly select points x_1, ..., x_n on interval [0, 1]. Expected value of largest distance between pairwise consecutive x_i.

Didn't know how to do any under time pressure, needed a lot of hints. No followup interview...