Quant Researcher Interview Questions from Point72
Quantitative researcher roles at top hedge funds like Point72 are among the most competitive and intellectually demanding positions in finance. The interview process is notorious for its rigor, testing not only mathematical prowess but also creativity, problem-solving, and a deep understanding of probability, statistics, and stochastic processes.
A basketball player is taking 100 free throws. She scores one point if the ball passes through the hoop and zero points if she misses. She has scored on her first throw and missed on her second. For each subsequent throw, the probability of her scoring is the fraction of throws she has made so far. For example, if she has scored 23 points after the 40th throw, then the probability that she will score in the 41st throw is \( \frac{23}{40} \). After 100 throws (including the first and the second), what is the probability that she scores exactly 50 baskets?
Let us define:
