Consider the following C program for producing Fibonacci numbers

Int Fibonacci(int n)

{ if (n <=011 n==1) return 1;

else  return Fibonacci(n-1)+Fibonacci(n-2);}

If for some large n, it takes 100 seconds to compute Fibonacci(n), how long will it take to compute Fibonacci(n+1), to the nearest second?

a. You got it.

b. I certainly was able to solve this stuff in high school but now I'm afraid to get a headache in the process. Run a MC simulation

Let's just stick to m=0 case where X_t is a standard BM.

Let tau =inf{t: X_t = 3 or X_t = -5}, tau1 = {t: X hit 3 before -5}, tau2={t: X hit -5 before 3}

Consider the martingale M_t = X_min{tau, t}, by Doob's sampling theorem E X_tau = X_0 =0. X_tau = 3 on {tau = tau1} and X_tau = -5 on {tau = tau2}; we get two equations

 P{tau=tau1}+P(tau=tau2) = 1

E X_tau = 0 can be written as

3P{tau = tau1} +(-5)*P{tau=tau2} = 0

you get P{X hit 3 before -5} = P{tau =tau1} = 5/8.

I remember seeing this (I think in mj's book) - the derivation took a few pages and involved 2 applications of Girsanov, one to remove the drift, one to put it back in.

Yeah the doob trick is neat, easy once you know how, and it did come up in an interview!

Everyone seems to have stories about tougher-than-hell interviews with Goldie Sticks. Are they really that bad or is there an element of myth involved here?

From the stories I've read here and at the other place it sounds like they have a 100 people grilling candidates for days, without any food or water, ask hard things, etc. You almost get the feeling that they have a dark room and one of these very bright lights in your eyes etc - sort of like the strategies carried out by the bad guys in a movie when they are trying to get information from some poor hero

Everyone seems to have stories about tougher-than-hell interviews with Goldie Sticks. Are they really that bad or is there an element of myth involved here?

I heard about a guy that had to spent his entire summer there from morning til night in a darkened room having to programme weird commodities sheaaa in a weird homemade script. Terrible. I don't know why anyone would put themselves through that. Maybe Patrik you heard a story like that too?