MML-10-03: Fisher Information, Observed Information & The Cramér-Rao Lower Bound – Practice Quiz

35 worked single-select and multiselect questions on Fisher Information, Observed Information & The Cramér-Rao Lower Bound. Intended level: Tier 3–4. Prerequisites: QS 10.2.

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: Prove score identities under stated regularity assumptions. Distinguish observed curvature from expected information. Compute information and variance bounds in ML sampling models. Use matrix information with nuisance parameters and correlations. Identify efficiency and derive equality conditions. Apply asymptotic normality with correct sample-size scaling. Diagnose nonregular support, boundaries and nonidentifiability.

Study references: Duke STA 611, Sampling Distributions of Estimators; Goodfellow, Bengio & Courville, Deep Learning.