Assess Fundamental Statistics Knowledge in Data-Science Interviews
Overview
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.
Google
Jul 12, 2025, 6:59 PM
Data Scientist
Technical Screen
Statistics & Math
6
0
Fundamental Statistics (Technical Phone Screen)
Context
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).
Questions
- Maximum Likelihood Estimation (Normal):
- Given an i.i.d. sample from a Normal distribution N(μ, σ²), derive the maximum-likelihood estimators (MLEs) for μ and σ².
- Conditional Density from a Joint Density:
- For continuous random variables X and Y with a known joint pdf f_{X,Y}(x, y), derive the conditional pdf f_{X|Y}(x | y).
- Standard Normal Distribution:
- Write the pdf φ(z) and cdf Φ(z) of the standard Normal distribution.
- Unbiasedness Assumptions (Concrete Task):
- Pick a concrete estimation task (e.g., estimating a population mean). List and justify the assumptions required for the estimator to be unbiased, and show a brief verification under those assumptions.
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