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Traditional Machine Learning

probability and statistics

Distributions, estimation, and uncertainty—how models reason about data and noise.

Beginner 18 hours · Self-paced 99.0 USD · 100 lessons · ~706 min read

20 topics 100 lessons Start anywhere
Grounded in sources, not a frozen script Ideas in this path map to readings and the Research Lab. See how we refresh lessons as the field moves.

What you’ll get out of this course

  • Build practical skill in “probability and statistics” with text-first lessons and clear checkpoints.
  • Level: Beginner—follow the syllabus in order or jump to the modules you need.
  • Reinforce ideas with end-of-topic checks and (where available) hands-on coding tasks.

Trust & quality

Content is designed and maintained by the Deep AI Minds team—structured for working adults, with frequent updates as tooling and best practices evolve.

Content currency: ~100% of lessons on the current curriculum revision

Instructor & outcomes

Deep AI Minds

Curriculum & instruction

Structured, industry-relevant paths with clear checkpoints and refresh cadence.

Satisfaction & billing

30-day satisfaction: if the syllabus or access is not as described, contact support and we will help (refunds for eligible purchases, case by case for integrations).

Common questions

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Syllabus

We structured this course to build your skills step by step

Scroll through each module below—open lessons in place or jump into a topic. Everything runs in order, but you’re free to explore.

Topic 1
Learning module

Probability foundations

Events, probability axioms, conditional probability, Bayes, independence.

Events and probability 7 min
Conditional probability 8 min
Bayes in practice 8 min
Independence and the product rule 7 min
Axioms and famous paradoxes 8 min
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Topic 2
Learning module

Combinatorics and counting

How to count without listing — permutations, combinations, inclusion–exclusion.

Counting principles 7 min
Permutations and arrangements 7 min
Combinations and the binomial coefficient 7 min
Inclusion–exclusion principle 8 min
Pigeonhole and its surprises 6 min
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Topic 3
Learning module

Random variables

From outcomes to numbers: discrete vs continuous, CDF/PDF, transformations.

Expectation and variance 7 min
Bernoulli and Gaussian (ideas) 8 min
Law of large numbers (intuition) 6 min
CDF and PDF 7 min
Transformations of random variables 8 min
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Topic 4
Learning module

Discrete distributions

Bernoulli, binomial, geometric, Poisson, categorical — the workhorse zoo.

Bernoulli deep dive 6 min
Binomial distribution 7 min
Geometric and negative binomial 7 min
Poisson distribution 7 min
Discrete uniform and categorical 6 min
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Topic 5
Learning module

Continuous distributions

Uniform, exponential, gamma, beta, normal, log-normal, heavy-tailed.

Uniform (continuous) 6 min
Exponential distribution 7 min
Gamma and beta distributions 8 min
Normal and log-normal 8 min
Heavy-tailed distributions 8 min
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Topic 6
Learning module

Joint and marginal distributions

Multiple random variables: joint, marginal, conditional, covariance.

Joint distributions 7 min
Marginalization 7 min
Conditional distributions 7 min
Covariance and correlation 7 min
Independence of random variables 7 min
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Topic 7
Learning module

Expectation, moments, and MGFs

Linearity of expectation, variance, higher moments, generating functions.

Expectation rules 7 min
Variance and higher moments 7 min
Moment generating functions 7 min
Characteristic functions 6 min
Laws of total expectation and variance 7 min
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Topic 8
Learning module

Limit theorems

Convergence, LLN, CLT, the delta method, concentration inequalities.

Types of convergence 7 min
Law of large numbers (formal) 7 min
Central limit theorem 8 min
The delta method 7 min
Concentration inequalities 8 min
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Topic 9
Learning module

Inference and testing

Sampling, confidence intervals, hypothesis tests, p-values, multiple testing.

Sampling and bias 7 min
Confidence intervals (intuition) 7 min
Hypothesis testing habits 7 min
p-values and significance 8 min
Multiple testing corrections 7 min
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Topic 10
Learning module

Maximum likelihood estimation

Likelihoods, MLE derivations, properties, Fisher information, Cramer–Rao.

Likelihood functions 7 min
MLE derivation walkthroughs 8 min
Properties of MLE 7 min
Fisher information 7 min
Cramer–Rao lower bound 7 min
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Topic 11
Learning module

Bayesian inference

Priors, likelihoods, posteriors, conjugate families, credible intervals.

Bayes' rule for inference 8 min
Priors and likelihoods 7 min
Posterior computation 8 min
Conjugate priors 7 min
Credible intervals 7 min
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Topic 12
Learning module

Regression statistics

Simple and multiple linear regression — assumptions, diagnostics, regularization.

Simple linear regression 7 min
Residuals and assumptions 7 min
Multiple regression 7 min
Regression diagnostics 7 min
Regularized regression — statistical view 7 min
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Topic 13
Learning module

ANOVA and categorical tests

One- and two-way ANOVA, chi-squared, Fisher exact, McNemar, paired tests.

One-way ANOVA 7 min
Two-way ANOVA 7 min
Chi-squared tests 7 min
Fisher's exact test 6 min
McNemar and paired tests 6 min
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Topic 14
Learning module

Resampling methods

Bootstrap, permutation tests, cross-validation, jackknife.

Bootstrap fundamentals 8 min
Bootstrap confidence intervals 7 min
Cross-validation as resampling 7 min
Permutation tests 7 min
Jackknife and bias correction 6 min
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Topic 15
Learning module

Stochastic processes basics

Random walks, Poisson processes, Brownian motion, stationarity, ergodicity.

What is a stochastic process? 6 min
Random walks 7 min
Poisson processes 7 min
Brownian motion (intuition) 7 min
Stationarity and ergodicity 7 min
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Topic 16
Learning module

Markov chains

Markov property, transition matrices, stationary distributions, mixing, HMMs.

The Markov property 6 min
Transition matrices 7 min
Stationary distributions 7 min
Mixing time and convergence 7 min
Hidden Markov models — intro 7 min
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Topic 17
Learning module

Monte Carlo methods

Monte Carlo integration, importance/rejection sampling, MCMC, Metropolis–Hastings.

Monte Carlo fundamentals 7 min
Importance sampling 7 min
Rejection sampling 7 min
MCMC intuition 7 min
Metropolis–Hastings 7 min
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Topic 18
Learning module

Statistical learning theory

ERM, VC dimension, bias–variance, generalization bounds, PAC learning.

Empirical risk minimization 7 min
VC dimension (intuition) 7 min
Bias–variance decomposition 7 min
Generalization bounds 7 min
PAC learning overview 7 min
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Topic 19
Learning module

Causal inference basics

Correlation vs causation, potential outcomes, RCTs, confounders, IVs.

Correlation vs causation 7 min
Potential outcomes framework 7 min
Randomized experiments 7 min
Confounders and adjustments 7 min
Instrumental variables 7 min
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Topic 20
Learning module

Statistics in practice

Reading papers, common fallacies, reproducibility, power, ML pipelines.

Reading statistical papers 7 min
Common statistical fallacies 7 min
Reproducibility and pre-registration 7 min
Power analysis and sample size 7 min
Statistics in ML pipelines 8 min
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