Solve core probability and statistics questions

Q: Solve core probability and statistics questions

This question evaluates proficiency in core probability and statistical inference—covering Bayes' rule, causal controls in regression, the Central Limit Theorem, uniform distribution moments, t-statistics, and minimum detectable effect—testing both conceptual understanding and practical computational fluency 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.

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Answer the following short theory/computation questions (as in an OA multiple-choice section). Provide the key formula and a brief explanation.

Bayes’ rule : Given a prior $P(A)$ , and likelihoods $P(B\mid A)$ , $P(B\mid A^c)$ , compute $P(A\mid B)$ .
Why add controls in regression? Explain when adding control variables helps estimate a causal effect, and when it can hurt.
CLT : State the Central Limit Theorem and what it implies about the sampling distribution of a sample mean.
Uniform distribution moments : For $X\sim \text{Unif}(a,b)$ , compute $E[X]$ and $\mathrm{Var}(X)$ .
Hypothesis testing / t-statistic : For comparing two means (or a regression coefficient), write the form of a t-statistic and how it’s used.
Effect size vs MDE : Relate effect size, variance, sample size, significance level $\alpha$ , and power $1-\beta$ to the minimum detectable effect (MDE).

Solve core probability and statistics questions

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