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Foundations: From Intuition to Mathematics
Probability, random variables, distributions, sampling distributions, the Central Limit Theorem, and standard errors. The bridge from DA-level intuition to DS-level rigor.
Module Content
From DA Stats to DS Stats — Why the Math Matters
The bridge from 'I read a dashboard' to 'I can write the maths'. What distinguishes DS-level statistics. FIND_VIDEO: search 'probability random variable expectation tutorial' — recommended channel: StatQuest / 3Blue1Brown. Aim for 10 min or under.
QUIZ: Probability, Random Variables, Expectations
Practice quiz: Three concepts that look obvious until you try to use them in a model. The mental model every DS interview probes.
Probability Distributions — Discrete and Continuous
The dozen distributions DS papers actually use. When each one shows up. FIND_VIDEO: search 'probability distributions normal binomial poisson' — recommended channel: StatQuest. Aim for 11 min or under.
QUIZ: The Distributions DS Actually Uses
Practice quiz: Eight distributions cover 95% of DS work. Memorize when each shows up and you'll read papers much faster.
Sampling Distributions and the CLT
Why everything is normal eventually. The most important theorem in applied statistics. FIND_VIDEO: search 'central limit theorem sampling distribution' — recommended channel: StatQuest / 3Blue1Brown. Aim for 11 min or under.
QUIZ: Why the Central Limit Theorem is Load-Bearing
Practice quiz: The CLT is why simple inference works even when the underlying data isn't normal. Internalize it once; use it forever.
Standard Errors and Estimators
Where the precision of any statistic comes from. The vocabulary every DS interview probes. FIND_VIDEO: search 'standard error estimator unbiased' — recommended channel: StatQuest. Aim for 10 min or under.
QUIZ: From Estimator to Confidence Interval
Practice quiz: An estimator is a recipe; the standard error tells you how reliable the recipe is. Confidence intervals package both.
SUBMISSION: Milestone Project 1 — Exploratory Distribution & Anomaly Analysis on Payment Fraud Data
Profile a 200K-row payments ledger: fit transaction-amount distributions, quantify tail risk with z-scores and IQR fences, and ship an anomaly-flagging notebook with a one-page fraud-ops memo.