Derive MLE and Bayesian posterior for Bernoulli
Company: OpenAI
Role: Machine Learning Engineer
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
Quick Answer: This question evaluates parameter estimation and inferential reasoning for Bernoulli/binomial data, including maximum likelihood estimation and its asymptotic variance, Bayesian updating with a Beta prior and the resulting posterior and posterior predictive probability, as well as interval estimation; it is classified in the Statistics & Math domain. It is commonly asked to assess understanding of frequentist versus Bayesian inference, the behavior and reliability of asymptotic approximations and credible intervals, and the practical implications for predictive probability and uncertainty quantification, testing both conceptual understanding and practical application.