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Answer core probability and statistics questions

NetflixData Scientist · Onsite
MediumData ScientistOnsiteStatistics & Math

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This question evaluates core probability and statistical inference competencies—covering Bayesian reasoning, regression controls and confounding, the Central Limit Theorem, distribution moments, t-statistics, and effect size/MDE—relevant to quantitative data analysis and hypothesis testing for a Data Scientist role in the Statistics & Math domain.

Answer the following interview-style probability/statistics questions. Provide formulas and short explanations.

  1. Bayes’ rule: State Bayes’ rule. Given a disease prevalence (P(D)=1%), a test sensitivity (P(+\mid D)=0.99), and false positive rate (P(+\mid\neg D)=0.05), compute (P(D\mid +)).

  2. Controls in regression: In an observational setting, why might adding control variables change the estimated coefficient on a variable of interest? When can adding controls introduce bias?

  3. CLT: State the Central Limit Theorem and its practical implication for the sampling distribution of the sample mean.

  4. Uniform distribution moments: If (X\sim \mathrm{Unif}(a,b)), compute (E[X]) and (\mathrm{Var}(X)).

  5. Hypothesis test / t-stat: For testing (H_0: \mu=\mu_0) with sample mean (\bar x), sample standard deviation (s), and sample size (n), write the one-sample t-statistic.

  6. Effect size vs MDE: Define effect size and Minimum Detectable Effect (MDE). How do power, variance, sample size, and alpha affect MDE?