: You break a stick at two random points chosen uniformly along its length. What is the probability that the three resulting pieces can form a triangle?

You roll a fair die repeatedly and add up the scores. You stop when the total is ≥21is greater than or equal to 21 . What is the most likely final sum?

Explain the Feynman-Kac formula and how it connects partial differential equations (PDEs) to stochastic processes.

: How does automatic garbage collection work in languages like Python or Java? Why do high-frequency trading (HFT) platforms avoid it?

: What is the Sherman-Morrison formula? How is it applied when making low-rank updates to an inverted covariance matrix?

These questions assess your theoretical knowledge of asset pricing models, risk neutral evaluation, and continuous-time finance. Brownian Motion & Itô’s Lemma

What is the gradient descent update rule? Under what conditions is it guaranteed to converge to a global minimum?

How do AIC and BIC penalize model complexity? Which one penalizes adding parameters more heavily as sample size grows? Machine Learning in Quant Finance Regularization (Lasso vs. Ridge): Compare L1cap L sub 1 (Lasso) and L2cap L sub 2

What is the Python GIL? How does it impact your ability to use multi-threading for CPU-bound quant research?

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