Think with rigor

Math, Statistics, and Probability

Refresh the mathematical intuition that supports metrics, optimization, uncertainty, and experimental reasoning.

Featured topics

4 topic cards built for interview prep

Each topic includes a summary, practical learning goals, representative interview prompts, and a suggested roadmap day.

Practice prompts

Daily-plan topics tied directly to this pillar

These are pulled from the same 133-day roadmap content used by Browse Questions.

Day 1Math · Probability fundamentals

Probability axioms, sample spaces, joint / marginal / conditional

  • What's the difference between joint, marginal and conditional probability — give a worked example?
  • When is independence the same as conditional independence? Why does the distinction matter for Naive Bayes?
Day 1Math · Probability fundamentals

Bayes' theorem: priors, likelihood, posterior

  • Walk through Bayes on a screening test (1% prevalence, 95% sensitivity, 90% specificity) — why is positive predictive value still low?
  • How would you use Bayes to update belief during an A/B test as data arrives?
Day 1Math · Probability fundamentals

Conditional probability traps & base-rate fallacy

  • Two children: at least one is a girl. What's the probability the other is also a girl? Defend your answer.
  • Why is P(disease|positive) ≠ sensitivity in general?
Day 2Math · Distributions you'll see in interviews

Bernoulli, Binomial, Poisson, Geometric — when to use which

  • When should you model click events as Bernoulli vs Poisson?
  • Derive the mean and variance of a Binomial(n, p).
Day 2Math · Distributions you'll see in interviews

Normal, Exponential, Uniform, Beta, Gamma — properties & use cases

  • Why is the Normal so common — what's the Central Limit Theorem intuition?
  • When would you pick a Beta distribution over a Normal?
Day 2Math · Distributions you'll see in interviews

Central Limit Theorem & Law of Large Numbers

  • State the Central Limit Theorem precisely and explain what it does NOT say.
  • How does the CLT justify using normal-based confidence intervals on means?
Day 3Math · Hypothesis testing & p-values

Null vs alternative, type I / II errors, power

  • Define Type I and Type II error and give an example where each is much more costly.
  • What does statistical power depend on, and how would you increase it?
Day 3Math · Hypothesis testing & p-values

P-values: what they mean and don't

  • What does a p-value of 0.03 actually mean? What does it NOT mean?
  • Walk me through the steps of a two-sample t-test on conversion rates.