This question evaluates fundamental statistics competencies including parameter estimation (MLEs for normal models), manipulation of joint and conditional densities, familiarity with the standard normal pdf and cdf, and estimator properties such as unbiasedness, and falls under the Statistics & Math domain.
You are given standard statistics tasks commonly used in a data-science interview. Assume all random variables and densities are well-defined and integrable where needed. For Question 1, let X₁, …, Xₙ be an i.i.d. sample from Normal(μ, σ²).
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