probability

Drawing a uniform sample from a stream too large for memory (or whose length stays unknown) is a genuine data-engineering problem. What interviewers watch for: the replace-with-decreasing-probability trick and a telescoping proof. Here is the answer.

A from-scratch staple that checks whether you grasp the conditional-independence assumption and why you work in log space. The signal is fitting per-class means and variances, summing log-likelihoods, and adding the log prior. Here is the implementation.

A standard stats question that also works as a numeracy check. The signal is linking MLE/MAP to regularization and getting the base-rate calculation right, the one that surprises most people. Here is the intuition along with the worked numbers.