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Probability and statistics for ML interviews

  • ML fundamentals
  • Asked often
  • About 1 h 35 min to learn
  • 3 vetted resources
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What this topic covers

The probability and statistics interviewers still screen for: conditional probability and Bayes' rule, the common distributions and when each applies, maximum likelihood as the idea behind every loss function you train, and basic frequentist tools such as confidence intervals, p-values and A/B test sizing. Questions are usually short puzzles (a rare-disease test, two children, expected waiting time) or a derivation (the MLE of an exponential or normal). The goal is fluent, correct reasoning out loud rather than memorised formulas.

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You’re ready when you can

What interviewers check, from the resources below.

  • Solve a rare-disease / false-positive Bayes question and explain why a second independent positive test changes the answer so much
  • Name the right distribution for counts in a time window, trials until first success, and a probability prior, with one-line justifications
  • Derive the MLE for an exponential or Bernoulli sample on paper
  • Explain what a 95% confidence interval does and does not mean, and sketch how you would size an A/B test
  • Explain, using the coin demo, why the posterior after one batch of flips is the prior for the next
  • Describe what a likelihood function is a function of, and why it is not a probability distribution over the parameter
  • Explain what happens to a confidence interval as sample size grows and why about 5% of 95% intervals miss the true value
  • Write the likelihood and log-likelihood for an i.i.d. sample and explain why the log is taken
  • Derive the MLE of the mean and variance of a normal sample and say which one is biased and by what factor
  • Explain why setting the derivative to zero can fail (integer parameters, maxima at endpoints)

What to study, in order

Each link opened and checked by hand; the date says when.

  1. Start here

    5.2 Probability and statistics (Introduction to Machine Learning Interviews Book) (opens in a new tab)

    huyenchip.com · Chip Huyen · 60 min · Free · checked 21 Oct 2026

    Why
    A concept checklist plus the actual style of question (rare-disease Bayes, German tank, coin-fairness, A/B sample size) that ML screens pull from, tagged by difficulty.
    What to read
    Read “5.2.1.1 Basic concepts to review” end to end, then work at least eight questions from “5.2.1.2 Questions” (cover the Bayes, distribution and MLE ones) and six from “5.2.2 Stats” (confidence intervals, p-values, A/B tests). Use the Next links to reach the question pages.
    What to skip
    The H-tagged puzzles on a first pass; the exponential-family paragraph unless you are targeting a research role.

  2. Free alternative

    Seeing Theory: A visual introduction to probability and statistics (opens in a new tab)

    Brown University · Daniel Kunin · 30 min · Free · checked 21 Oct 2026

    Why
    If Bayes' rule, likelihood or confidence intervals feel like formulas rather than pictures, these interactive demos fix the intuition in under half an hour.
    What to read
    Chapter 3 “Probability Distributions” (all three sections), Chapter 4 “Frequentist Inference” sections “Point Estimation” and “Interval Estimation”, and Chapter 5 “Bayesian Inference” (“Bayes' Theorem”, “Likelihood Function”, “Prior to Posterior”).
    What to skip
    Chapters 1, 2 and 6 (basics, counting, regression) unless you are rusty on expectation and variance.

  3. Go deeper

    8.2.3 Maximum Likelihood Estimation (Introduction to Probability, Statistics, and Random Processes) (opens in a new tab)

    probabilitycourse.com · Hossein Pishro-Nik · 35 min · Free · checked 21 Oct 2026

    Why
    “Derive the MLE” is the one probability question that reliably appears in ML screens, and this is the cleanest worked treatment with binomial, exponential and normal examples.
    What to read
    Read “8.2.3 Maximum Likelihood Estimation” fully, working each example before reading its solution, then the short “8.2.4 Asymptotic Properties of MLEs” page via the next link. If Bayes' rule is shaky, read “1.4.3 Bayes' Rule” first.
    What to skip
    The end-of-section solved problems and anything on moment-matching estimators.

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