Sample Question #138 (mathematics – stochastics)
(The interviewer shows you a line chart that looks like a stock price chart, but with the y-axis labeled "50, 55, 60, 65," i.e., the smallest value on the line is no less than 10. The x-axis is unlabeled.)
This chart shows a random walk in progress. Now, answer the following:
1. What does the x-axis represent?
2. What’s the probability that this random walk will hit 0? How about -2,000?
3. If I tell you that the terminus of the random walk line represents its state at time t1, what’s the probability that the random walk will hit 0 by some later time t2 > t1?
(Comment: random walk questions are quite popular with quant interviewers, so you should know at least some basics)