Answer core probability and statistics questions

Q: Answer core probability and statistics questions

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.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

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

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 $P(D\mid +)$ .
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?
CLT: State the Central Limit Theorem and its practical implication for the sampling distribution of the sample mean.
Uniform distribution moments: If $X\sim \mathrm{Unif}(a,b)$ , compute $E[X]$ and $\mathrm{Var}(X)$ .
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.
Effect size vs MDE: Define effect size and Minimum Detectable Effect (MDE). How do power, variance, sample size, and alpha affect MDE?

Answer core probability and statistics questions

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