MML-10-02: Maximum Likelihood Estimation (MLE): Likelihood, Log-Likelihood & Score Function – Practice Quiz

45 worked single-select and multiselect questions on Maximum Likelihood Estimation (MLE): Likelihood, Log-Likelihood & Score Function. Intended level: Tier 2–4. Prerequisites: QS 10.1, Part 06.

The sequence develops conceptual interpretation, explicit calculations, ML diagnostics and, where assigned, derivations with carefully stated assumptions. Feedback explains each answer and misconception by content.

Learning objectives: Form likelihood and log-likelihood functions from an explicit sampling model. Compute scores and evaluate boundary and interior candidates. Derive Bernoulli and categorical probability estimates. Derive Poisson and exponential rate estimates. Derive Gaussian mean and variance estimates. Connect conditional likelihood to ML losses and numerical stability. Distinguish existence, identifiability and global optimality. Prove parameter-transformation and sufficient-statistic results.

Study references: Pishro-Nik, Introduction to Probability, Statistics, and Random Processes; Goodfellow, Bengio & Courville, Deep Learning.