Question #1 (statistics)
How do you test whether a data sample is normal or not?
(Comment: this tests your knowledge in basic statistics; there are several different methods to test normality.)
Question #2 (math)
Show that a set is convex if and only if its intersection with any line is convex. Show that a set is affine if and only if its intersection with any line is affine.
(Taken from chapter 2 of Boyd and Vandenberghe, Convex Optimization)
(Comment: concepts related to convex sets are important in optimization, and many quant jobs involve optimization research.)
Question #3 (finance - bond pricing)
I don't know anything about bond pricing, but I've heard people use something called the discount rate when they price bonds. Can you explain what this "discount rate" is? Why is it important? Where do I get its value? What is the current discount rate (as of today)? When I price a 30-year bond, should I use today's discount rate or should I use a different discount rate for each of the next 30 years?
(Comment: typical set of basic questions asked at a lot of quant interviews, not just those for fixed income-related positions)
Question #4 (probability theory)
Say you are on a game show [historical sidenote: this question was first played on the 60s American game show Let's Make a Deal, hosted by Monty Hall], and there are three closed doors. Behind one door is a car, the prize you dream of, and behind the other two are goats. You pick a door. The host, who knows what's behind each door, opens another which reveals a goat. Now, the host lets you make another choice: should you stick with you first door choice, or should you switch and pick a different door, in order to win the car?
Question #5 (applied math)
What's a Hermitian matrix? What important property does a Hermitian matrix's eigenvalues possess? What's the practical implication of this property in applications?
