OpenAI·Machine Learning Engineer·Technical Phone Screen
- Given n Bernoulli trials with k successes, derive the maximum likelihood estimator for the success probability p and describe its asymptotic variance.
- With a Beta(alpha, beta) prior on p, derive the posterior distribution and compute the posterior predictive probability of success on the next trial.
- Construct a 95% confidence interval for p using a normal approximation, and separately a 95% credible interval from the posterior. Walk through both.
- When is each type of interval actually reliable, and how does sample size change the picture for both frequentist and Bayesian inference?
“The MLE derivation itself is straightforward, k/n, anyone who's taken a stats course gets there.”