Interview Question: Random Certainty

Sample Question #222 (mathematics – stochastics)

How would you prove that the probability of a random walk hitting any arbitrary number is 1?

(Hint: when you’re asked "how would you prove…", you’re expected to give a sketch of a proof, not the proof itself. Some interviewers would actually be pissed if you gave a formal proof, believing you didn’t understand what they were looking for. So, always answer the question in the form the interviewer wants — and this means you must listen to the questioning very carefully.)

Advertisements
This entry was posted in Sample Qs. Bookmark the permalink.

One Response to Interview Question: Random Certainty

  1. Unknown says:

    If there is a number (call it ‘a’) which is hit with probability <1 then it ‘a’ is NOT hit with positive probability. Since the paths of Brownian motion are continuous, with positive probability they stay bounded by ‘a’. But this is impossible because the variance must grow with time (sigma^2*t) which won’t happen if a path is bounded by ‘a’.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s