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LeadAfrik
Intermediate · Self-paced2026 Edition

Probability & Statistics for Finance

The probability and statistics a quant or risk analyst must own — distributions, MLE, hypothesis testing, Bayesian updating, multivariate normality, copulas, and extreme-value theory. Twelve modules taught from the standpoint of a working desk: why log returns are nearly normal until they aren't, why correlation collapses in a crisis, and the small set of distributions that cover 95% of real return modelling.

12

Modules

~11h 15m

Reading time

Intermediate

Level

Self-paced

Format

§

Syllabus

  1. 01

    Probability foundations

    Sample spaces, events, axioms, conditional probability, Bayes' rule. The vocabulary every later module assumes.

    ~50 minModule 01
    →
  2. 02

    Random variables and expectation

    Discrete vs continuous, CDF, PDF, PMF. Expectation, variance, moments. The linearity-of-expectation trick that saves work.

    ~55 minModule 02
    →
  3. 03

    The eight distributions a quant actually uses

    Normal, lognormal, Student-t, Bernoulli, binomial, Poisson, exponential, beta — what each models, where each fails.

    ~60 minModule 03
    →
  4. 04

    Joint distributions, dependence, copulas

    Joint, marginal, conditional. Covariance and correlation as linear-only measures. Copulas and tail dependence — why Gaussian correlation lied in 2008.

    ~60 minModule 04
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  5. 05

    LLN, CLT, and modes of convergence

    Weak vs strong LLN. Classical CLT, the Berry-Esseen rate, and why the CLT is the licence to use the normal at all.

    ~55 minModule 05
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  6. 06

    Estimation — MLE, MoM, and properties

    Estimators as random variables. Method of moments, maximum likelihood. Bias, consistency, efficiency, the Cramér-Rao bound.

    ~60 minModule 06
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  7. 07

    Hypothesis testing without the cargo cult

    What a p-value really says, type I/II errors, power, multiple testing. The hypotheses a desk quant actually tests.

    ~55 minModule 07
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  8. 08

    Bayesian inference

    Bayes' rule as belief updating. Conjugate priors. Posterior predictive. Why Black-Litterman is Bayesian portfolio construction.

    ~60 minModule 08
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  9. 09

    Regression as a statistical estimator

    OLS as MLE under Gaussian errors. Sampling distribution of β̂, standard errors, the t/F machinery, R² done honestly.

    ~55 minModule 09
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  10. 10

    The multivariate normal

    Mean vector, covariance matrix. Marginal and conditional distributions. Mahalanobis distance. Why so much quant assumes MVN.

    ~55 minModule 10
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  11. 11

    Bootstrap and resampling

    Nonparametric inference. Percentile, BCa, block bootstrap for time-series. When the bootstrap saves you and when it doesn't.

    ~50 minModule 11
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  12. 12

    Heavy tails, EVT, VaR and CVaR

    Why returns aren't normal. Generalised extreme value, Pareto tails, peak-over-threshold. Computing VaR and CVaR three ways.

    ~60 minModule 12
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How to use this course

Start with module 01 if the material is new; skip ahead if you have prior exposure. Each module is self-contained but the arc is sequential — the projects in the final module assume the toolkit from modules 1-11. Every module ends with key takeaways and a curated further-reading list with primary sources.