Quick Reference & Tips

You should have the key formulas internalized (Bayes' theorem, binomial PMF, normal 68-95-99.7 rule, sample size formula) but you do not need to memorize proofs. Interviewers care more about when to apply each formula and why it works than about perfect recall. If you forget a specific formula, say "I know this involves the ratio of between-group and within-group variance" and the interviewer will usually help with the exact notation. Understanding beats memorization every time.

Data Scientist: Heavy emphasis on hypothesis testing, A/B testing, experimental design, causal inference, and communicating statistical results to stakeholders. You will likely be asked to design an experiment, choose metrics, calculate sample sizes, and interpret results. Companies like Meta and Airbnb weight this heavily.

ML Engineer: More focus on probability (distributions, Bayes, information theory) and how it connects to ML algorithms. Less experimental design, more mathematical foundations. Questions might involve deriving loss functions, understanding probabilistic models, or explaining why certain algorithms work. Google and DeepMind lean this direction.

Both. Most companies test frequentist methods (hypothesis testing, p-values, confidence intervals) because that is what their A/B testing platforms use. However, Bayesian concepts (priors, posteriors, Bayes' theorem) come up in algorithm questions and are increasingly used in industry (Thompson sampling, Bayesian optimization, Bayesian A/B testing). A strong candidate can explain the same concept from both perspectives and articulate when each is more appropriate. Start with frequentist if you are short on time, but do not skip Bayes' theorem.

Start with the 15 puzzles in Lesson 6 of this course. For each puzzle: (1) try to solve it yourself for 10 minutes, (2) read the solution carefully, (3) identify the technique used (complement counting, recursion, symmetry, conditional probability), (4) redo it from memory the next day. After mastering these, work through "Fifty Challenging Problems in Probability" by Mosteller. The key is recognizing patterns: most puzzles use one of about 8 standard techniques. Once you see the pattern, the solution becomes straightforward.

Extremely important for data science roles. At Meta, Google, Amazon, Netflix, and Uber, nearly every data scientist is involved in A/B testing. You should be able to: (1) design an experiment from scratch (hypothesis, metrics, sample size, duration), (2) identify common pitfalls (peeking, multiple testing, network effects, novelty effects), (3) interpret results correctly (effect size vs statistical significance), and (4) explain advanced techniques (CUPED, sequential testing, multi-armed bandits). For ML engineering roles, basic A/B testing knowledge is still expected, but the depth is less.

Stay calm and work from first principles. For example, if asked to derive the variance of the sample mean: "I know variance measures spread. The sample mean averages n observations. If observations are independent with variance σ², then Var(sum) = nσ², and Var(mean) = Var(sum/n) = nσ²/n² = σ²/n." Walking through the logic step by step is more impressive than reciting a memorized derivation. If you are truly stuck, say "I know the result is σ²/n but let me think about the derivation..." Most interviewers will give you a hint to move forward.

Ad Tech (Google, Meta): CTR modeling, auction theory, bid optimization, attribution modeling.
E-commerce (Amazon, Shopify): Demand forecasting, price elasticity, conversion funnel analysis, inventory optimization.
Ride-sharing (Uber, Lyft): Surge pricing, marketplace experiments (two-sided), spatial statistics, ETA estimation.
Healthcare: Survival analysis, clinical trial design, multiple endpoint testing, regulatory requirements for statistical evidence.
Finance: Value at Risk (VaR), heavy-tailed distributions, time series analysis, Monte Carlo simulation. For all industries, the core probability and hypothesis testing skills are the same — only the applications differ.