Course
Probability for
Quants
Learn to model uncertainty, condition on information, work with distributions and dependence, approximate and simulate responsibly, and apply probability to unfamiliar quant interview and research problems.
Beginner → Advanced
4 Progressive Phases
22 Modules
106 Lesson Units
QT + QR Paths
Research Depth Extensions
Learning Outline
Prerequisite Bridges
Prerequisite Bridges
Prerequisite Bridges
Prerequisite Bridges
Module 1
Mathematical and computational bridges
6 lessons
Module 1
Mathematical and computational bridges
1.1Algebra, functions and notation
1.2Sums, products, sequences and recurrences
1.3Calculus for one random variable
1.4Vectors and matrices for probability
1.5Multivariable calculus and regions
1.6Python for probability experiments
Phase 1
Interview Foundations
Phase 1
Interview Foundations
Module 2
Probability models, events and modelling assumptions
4 lessons
Module 2
Probability models, events and modelling assumptions
2.1Experiments, outcomes and sample spaces
2.2Event algebra and probability axioms
2.3Complements, inclusion–exclusion and bounds
2.4Symmetry and the meaning of “random”
Module 3
Counting and combinatorial probability
5 lessons
Module 3
Counting and combinatorial probability
3.1Product and sum principles
3.2Permutations and repeated objects
3.3Combinations, allocations and stars and bars
3.4Restricted counting and inclusion–exclusion
3.5From counts to probabilities
Module 4
Conditioning, independence and information
5 lessons
Module 4
Conditioning, independence and information
4.1Conditional probability and the chain rule
4.2Total probability and Bayes’ theorem
4.3Independence, mutual independence and exchangeable symmetry
4.4Conditional independence
4.5Observation mechanisms and sequential evidence
Module 5
Random variables, expected value and variance
5 lessons
Module 5
Random variables, expected value and variance
5.1Random variables and discrete distributions
5.2Expected value, payoff and profit
5.3Linearity and the expected-value rule
5.4Variance, standard deviation and moments
5.5Conditioning to calculate expectation
Module 6
Essential discrete distributions
5 lessons
Module 6
Essential discrete distributions
6.1Indicators, Bernoulli and categorical outcomes
6.2Binomial versus hypergeometric
6.3Geometric and negative binomial
6.4Poisson counts and rare-event reasoning
6.5Multinomial counts
Module 7
Expectation-based interview problem solving
5 lessons
Module 7
Expectation-based interview problem solving
7.1Indicator decompositions
7.2Tail-sum expectation
7.3Recursive waiting times and pattern states
7.4Coupon collection, records and symmetry
7.5Simple decisions under uncertainty
Phase 2
Mathematical Probability
Phase 2
Mathematical Probability
Module 8
Continuous probability, tails and survival
4 lessons
Module 8
Continuous probability, tails and survival
8.1Densities, CDFs, quantiles and mixed distributions
8.2Continuous expectation and tail integrals
8.3Uniform models and geometric probability
8.4Survival, hazard and residual life
Module 9
Essential continuous distribution families
5 lessons
Module 9
Essential continuous distribution families
9.1Exponential, gamma and chi-square
9.2Normal distributions and standardisation
9.3Beta distributions
9.4Lognormal distributions and multiplicative outcomes
9.5Heavy tails and nonexistent moments
Module 10
Joint distributions and dependence
5 lessons
Module 10
Joint distributions and dependence
10.1Joint PMFs and random vectors
10.2Joint densities and support
10.3What independence does and does not imply
10.4Covariance, correlation and aggregate variance
10.5Covariance matrices and valid dependence models
Module 11
Conditional distributions, conditional moments and prediction
6 lessons
1 Research Depth
Module 11
Conditional distributions, conditional moments and prediction
11.1Conditional PMFs, PDFs and truncation
11.2Conditional expectation as a random variable
11.3Conditional variance and total variance
11.4Mixtures and elementary Bayesian probability models
11.5Random sums and compound distributions
11.6Conditional expectation as the best squared-error predictor
Module 12
Functions, sums and transformations of random variables
5 lessons
QR Core
Module 12
Functions, sums and transformations of random variables
12.1The CDF method
12.2Monotone and non-monotone transformations
12.3Sums, differences and convolution
12.4Multivariable transformations
12.5Probability integral transforms and inverse sampling
Module 13
Order statistics, extremes and races
4 lessons
1 Research Depth
Module 13
Order statistics, extremes and races
13.1Minima and maxima
13.2The \(k\)-th order statistic
13.3Joint order statistics, ranges and spacings
13.4Exponential races
Module 14
Gaussian vectors and linear prediction
5 lessons
2 Research Depth
Module 14
Gaussian vectors and linear prediction
14.1Constructing multivariate normals
14.2Gaussian closure and independence
14.3Bivariate Gaussian conditioning
14.4Multivariate Gaussian conditioning
14.5Linear models, projections and quadratic forms
Phase 3
Approximation & Computation
Phase 3
Approximation & Computation
Module 15
Generating functions and distributional structure
4 lessons
1 Research Depth
Module 15
Generating functions and distributional structure
15.1Probability generating functions
15.2Moment generating functions and their limitations
15.3Characteristic functions and cumulants
15.4Compound distributions and method selection
Module 16
Inequalities, convexity and tail bounds
4 lessons
1 Research Depth
Module 16
Inequalities, convexity and tail bounds
16.1Markov, Chebyshev and one-sided bounds
16.2Jensen’s inequality and nonlinear expectations
16.3Cauchy–Schwarz and covariance constraints
16.4Chernoff and Hoeffding bounds
Module 17
Convergence, large numbers and approximations
6 lessons
2 Research Depth
Module 17
Convergence, large numbers and approximations
17.1What convergence means
17.2Weak and strong laws of large numbers
17.3The central limit theorem
17.4Choosing and checking approximations
17.5Transforming asymptotic results
17.6When limits and expectations do not commute
Module 18
Simulation and Monte Carlo reasoning
7 lessons
2 Research Depth
Module 18
Simulation and Monte Carlo reasoning
18.1Reproducible random experiments
18.2Inverse transforms and distribution generators
18.3Acceptance–rejection sampling
18.4Simulating Gaussian vectors
18.5Monte Carlo estimates and error bars
18.6Variance reduction
18.7Importance sampling
Phase 4
Sequential Probability & Quant Applications
Phase 4
Sequential Probability & Quant Applications
Module 19
Finite-state Markov chains and random walks
5 lessons
Module 19
Finite-state Markov chains and random walks
19.1States, transitions and the Markov property
19.2First-step analysis and gambler’s ruin
19.3Stationary distributions versus limiting distributions
19.4Occupation counts and accumulated rewards
19.5Simulation and balance
Module 20
Arrival counts, waiting times and random incidence
4 lessons
1 Research Depth
Module 20
Arrival counts, waiting times and random incidence
20.1From Poisson counts to a Poisson process
20.2Superposition, thinning and competing streams
20.3Conditioning on counts and compound arrivals
20.4Inspection paradox and length-biased sampling
Module 21
Information, stopping and sequential decisions
4 lessons
1 Research Depth
Module 21
Information, stopping and sequential decisions
21.1Information through time and stopping times
21.2Martingales and bounded stopping
21.3Wald’s identity and stopped sums
21.4Finite-horizon optimal decisions
Module 22
Integrated quant probability capstones
3 lessons
Module 22
Integrated quant probability capstones
22.1Signals, selection and conditional expected payoff
22.2Multivariate risk and simulation report
22.3Unseen problems and assumption defence
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