Google·Data Scientist·Technical Phone Screen
May 2026
A stats-heavy Google data scientist interview that was basically a probability theory exam. Four parts covering normal distributions, MLE derivations, bivariate conditionals, and bias correction. No behavioral fluff, just math.
- Write the pdf and cdf of a Normal distribution with mean μ and variance σ², then express P(μ − σ ≤ X₁ ≤ μ + σ) in terms of the standard Normal cdf Φ.
- Derive the MLEs of μ and σ² under three scenarios: σ² known, both unknown, and μ constrained to be non-negative. For the constrained case, explain what the MLE is when the unconstrained estimate is negative.
- For a bivariate Normal (X, Y), derive the conditional distribution of X given Y = y. Give the conditional mean, variance, pdf, and cdf, then compute P(X > t | Y = y) using Φ.
- Is the standard MLE of σ² unbiased? If not, what is an unbiased estimator, and how does it relate to the MLE?
“This felt like a warmup but I fumbled the cdf notation at first, wrote it without the standardization step and had to backtrack.” The rest of the author's notes on Data Scientist interview at Google, Technical Phone Screen round, covers how they worked through the question, what the panel pushed back on, and what they would do differently.
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