Stop nodding along at p-values and confidence intervals — build the intuition to design a study, run the test, and defend the answer.
You can run a t-test in three lines of Python and still have no idea whether the answer means anything. That gap — tools without understanding — is where bad decisions get made: A/B tests called early, confidence intervals read as probabilities, models that fit noise. This course closes it by rebuilding probability and statistics from the ground up, one runnable problem at a time. You start with sample spaces and the three axioms, because most probability mistakes are really bookkeeping mistakes. Then random variables, moments, and the tail bounds that give you guarantees when the distribution is unknown. Modules 4 to 6 cover the named distributions you will actually fit — Poisson counts, heavy-tailed latencies, correlated pairs — with goodness-of-fit tests to check your choice. Modules 7 to 10 build the inference machinery: the central limit theorem and why it works, maximum likelihood and confidence intervals, testing with honest power analysis, and Bayesian methods through MCMC and PyMC. Every module ends with a project that leaves you an artifact: fitted models, plotted bounds, a written defense of your methodology. No calculus needed for the first four modules.
Built by Lakshya Kumar
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Once uncertainty has a number attached you can average it, spread it, and transform it — and every later module runs on that move.
Shape statistics say what a distribution usually does; a handful of inequalities say what it can do at worst, assuming almost nothing.
Most counting problems are one of seven named distributions in disguise, and spotting which one saves you from deriving it by hand.
Latencies, file sizes and waiting times are rarely normal — learn to pick, fit and defend the curve your data actually follows.
Correlation is only one shape of dependence; here you test for independence properly and see what a scatter plot quietly hides.
The central limit theorem is why almost every test you will ever run works — and knowing its rate tells you when it does not.
You never get the population, only a sample — this is how you turn one into a defensible number with honest error bars attached.
Significance is not importance; learn power, error rates and multiple-testing corrections so your results survive real scrutiny.
Priors let you start from what you already know, and MCMC fits models no closed form can reach — even when the data set is small.
Complete all modules, then submit the required number of capstone projects. Each must earn a passing rating from an admin reviewer.
Identify a measurable phenomenon you care about, collect or simulate data, perform a full statistical analysis (exploratory, hypothesis test, and Bayesian update), and write a 6–10 page report defending your methodology and conclusions.
I'm studying Probability & Statistics: sample spaces, random variables, expectation, common distributions (Binomial, Normal, Poisson, Exponential, Beta, Gamma), the Central Limit Theorem, hypothesis testing (t-tests, chi-squared, ANOVA, multiple testing), and Bayesian inference (priors, posteriors, MCMC). Context: 1. My background: [e.g. "software engineer who uses ML libraries but doesn't understand the math", "data analyst who runs tests but doesn't understand p-values"] 2. What I want to be able to do: [e.g. "design A/B tests I trust", "understand confidence intervals", "build Bayesian models in PyMC"] 3. One concept I'm stuck on: [e.g. "I can calculate p-values but don't understand what they mean"] Answer: - Given my background, should I start at Module 1 or skip ahead? - For the concept in (3): give me a concrete two-paragraph intuition plus a Python snippet I can run. - What's the single most important practical skill from this course for goal (2)?
Concise graduate-level reference. Pair with Modules 6–10.