D'Math University | Statistics & Data Science  ·  Programme #17

BSc Probability & Statistics

A focused double-discipline undergraduate programme that builds mastery in both classical probability theory and mathematical statistics. Four specialist tracks — actuarial, financial, computational, and applied — allow students to tailor their degree to their ambitions.

Undergraduate 3 Years Online Theory & Application
28
Modules Available
£40k
Average Graduate Salary
38+
Partner Universities
4
Specialist Tracks

Programme Overview

The BSc Probability & Statistics is the ideal degree for students who love the mathematical depth of probability theory alongside the applied power of statistical science. Year 1 covers classical probability, combinatorics, and introductory statistics. Year 2 advances to measure-theoretic probability, stochastic processes, and statistical inference. Year 3 allows specialisation across four tracks: Actuarial, Financial, Computational, and Applied Probability and Statistics.

The actuarial track aligns closely with IFoA and CAS CT-series exam content, giving students a significant head-start on the path to full actuarial qualification.

What You'll Learn

  • Classical Probability: Combinatorics, conditional probability, distributions, generating functions
  • Measure-Theoretic Probability: Sigma-algebras, Lebesgue integration, convergence theorems
  • Stochastic Processes: Markov chains, Poisson processes, Brownian motion
  • Statistical Inference: Point estimation, hypothesis tests, confidence regions
  • Monte Carlo Methods: Simulation, variance reduction, MCMC fundamentals
  • Random Graphs & Networks: Erdos-Renyi models, scale-free networks, percolation
  • Actuarial Probability: Ruin theory, risk models, life tables, and loss distributions
  • Statistical Computing: Simulation studies, bootstrap, numerical methods in R
Core Curriculum
🎲

Classical Probability

Foundations of probability: sample spaces, events, conditional probability, Bayes' theorem, and classical distributions.

📊

Mathematical Statistics

Formal statistical theory — estimation, testing, confidence intervals, and sufficiency within the framework of statistical models.

🔢

Measure-Theoretic Probability

Probability on abstract spaces — sigma-algebras, random variables as measurable functions, Lebesgue integrals, and L^p spaces.

📈

Stochastic Processes

Markov chains (discrete and continuous), Poisson processes, Brownian motion, and martingales with financial applications.

🧮

Random Graphs & Networks

Probabilistic models of networks — Erdos-Renyi, Barabasi-Albert, connectivity thresholds, and spectral graph theory.

🔬

Statistical Inference

Likelihood theory, uniformly most powerful tests, the Neyman-Pearson lemma, and non-parametric alternatives.

📐

Monte Carlo Methods

Simulation techniques, importance sampling, stratified sampling, MCMC (Metropolis-Hastings, Gibbs), and variance reduction.

🧬

Actuarial Probability

Risk models, ruin theory, survival models, life tables, and loss distributions aligned to IFoA actuarial examination content.

Course Catalogue

Click any course to view its objective and learning outcomes.

PST 101 Probability Theory I +

Objective

To establish the axiomatic theory of probability.

Learning Outcomes

  • Apply Kolmogorov's axioms.
  • Compute probabilities of compound and conditional events.
  • Use random variables and distribution functions.
  • Compute moments and moment generating functions.
  • Identify common discrete and continuous distributions.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
PST 102 Statistical Inference I +

Objective

To estimate parameters and test hypotheses using frequentist methods.

Learning Outcomes

  • Estimate parameters using MLE and method of moments.
  • Apply Cramér-Rao bound.
  • Conduct Neyman-Pearson hypothesis tests.
  • Construct confidence intervals.
  • Interpret p-values and errors correctly.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
Interactive Activity — Hypothesis Testing Visualizer
Set null hypothesis μ₀, sample mean x̄, sample size n and σ. The activity computes the z-statistic, p-value (shaded tail), and tells you whether to reject H₀ at significance α.
μ₀ = x̄ = σ = n =
α = 0.050 Tail:
PST 103 Linear Algebra +

Objective

To establish matrix algebra as the foundation for multivariate statistics.

Learning Outcomes

  • Solve linear systems via factorisation.
  • Compute eigendecomposition and SVD.
  • Apply quadratic forms to statistics.
  • Use projections in regression theory.
  • Implement matrix algorithms.
Interactive Activity — 2×2 Matrix Transformation
Set the entries of a 2×2 matrix. Watch how it transforms the unit square. Determinant = signed area of the transformed square.
a = 1.0 b = 0.5 c = -0.3 d = 1.0
PST 104 Calculus +

Objective

To master differential and integral calculus needed for probability theory.

Learning Outcomes

  • Compute partial derivatives and gradients.
  • Apply Lagrange multipliers.
  • Use multivariable integration.
  • Apply Taylor series.
  • Verify convergence of integrals and series.
Interactive Activity — Derivative as Slope of Tangent
Drag the slider to move point P along the curve. The tangent line updates — its slope is the derivative.
f(x): x = 1.00
Interactive Activity — Riemann Sum Approximation
Drag the slider to add more rectangles. Watch the approximation converge to the true integral.
Rectangles n = 8
PST 201 Probability Theory II — Measure-Theoretic +

Objective

To formalise probability through measure theory and Lebesgue integration.

Learning Outcomes

  • Apply Borel sets and measurable functions.
  • Define expectation as a Lebesgue integral.
  • Apply convergence theorems including dominated convergence.
  • Prove the strong law of large numbers.
  • State and apply martingale concepts.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
PST 202 Statistical Inference II +

Objective

To extend inference to likelihood ratio tests and asymptotic theory.

Learning Outcomes

  • Apply likelihood ratio tests.
  • Use asymptotic distributions of MLE.
  • Apply UMP and unbiased tests.
  • Use sufficient and complete statistics.
  • Apply Bayesian decision theory.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
Interactive Activity — Hypothesis Testing Visualizer
Set null hypothesis μ₀, sample mean x̄, sample size n and σ. The activity computes the z-statistic, p-value (shaded tail), and tells you whether to reject H₀ at significance α.
μ₀ = x̄ = σ = n =
α = 0.050 Tail:
PST 203 Linear Models & Regression +

Objective

To estimate, diagnose and select among linear models.

Learning Outcomes

  • Fit OLS regression and interpret coefficients.
  • Diagnose violations of assumptions.
  • Apply variable selection and regularisation.
  • Use generalised linear models.
  • Build prediction models with cross-validation.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
Interactive Activity — Linear Regression (Drag-and-Drop)
Click the canvas to add scatter points. The least-squares line, equation, and R² update live. Vertical lines from each point show residuals.
Click to add points (need at least 2 for a line).
PST 204 Bayesian Statistics +

Objective

To apply Bayesian reasoning to inference and decision-making.

Learning Outcomes

  • Apply Bayes' theorem with conjugate priors.
  • Construct posterior distributions.
  • Apply MCMC for posterior simulation.
  • Apply Bayesian model comparison.
  • Discuss the philosophy of Bayesian inference.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
Interactive Activity — Bayesian Coin Update
Beta(α, β) prior on a coin's bias. Click "Toss" to flip a coin (true bias hidden) and watch the posterior update via Bayes' rule.
prior α = 1.0 prior β = 1.0
true p =
Toss the coin to start updating the posterior.
PST 301 Stochastic Processes +

Objective

To analyse processes evolving in time including Markov chains and Brownian motion.

Learning Outcomes

  • Analyse discrete and continuous Markov chains.
  • Apply Poisson processes.
  • Use Brownian motion in modelling.
  • Analyse martingales and stopping times.
  • Apply queueing theory.
Interactive Activity — Distribution Plotter
Pick a distribution and adjust its parameters. Read off mean and variance directly from the plot.
Distribution: p1 = 0.0 p2 = 1.0
Interactive Activity — Central Limit Theorem Simulator
Sample n values, take their average, repeat. The histogram of averages converges to a normal distribution — CLT in action.
Source: Sample size n = 10
Total sample means: 0
PST 302 Multivariate Statistics +

Objective

To analyse data with many variables using rigorous statistical methods.

Learning Outcomes

  • Apply PCA and factor analysis.
  • Use canonical correlation analysis.
  • Apply MANOVA and discriminant analysis.
  • Apply clustering methods.
  • Visualise high-dimensional data.
PST 303 Computational Statistics +

Objective

To use simulation and numerical methods in statistics.

Learning Outcomes

  • Apply bootstrap and Monte Carlo methods.
  • Implement MCMC algorithms.
  • Use EM and variational inference.
  • Apply numerical optimisation.
  • Build reproducible computational reports.
Interactive Activity — Vector Field & Gradient Visualizer
Pick a scalar field f(x,y). Gradient arrows point in the direction of steepest ascent. Click anywhere to drop a particle that follows the gradient.
f(x,y) =
Click on the plot to drop a particle.
PST 304 Statistics Capstone Project +

Objective

To pursue an extended applied statistics project under supervision.

Learning Outcomes

  • Frame a real-world problem statistically.
  • Acquire and clean appropriate data.
  • Apply rigorous statistical methods.
  • Write a research-style statistical report.
  • Present findings to a non-technical audience.
Career Pathways
📐

Actuary

Model financial risk for insurance, pensions, and investment firms, progressing through IFoA or CAS qualification examinations.

⚠️

Risk Analyst

Quantify and manage operational, market, and credit risk at banks, insurance companies, and regulatory bodies.

📊

Statistician

Design studies and analyse data in government, academia, healthcare, or private sector analytics teams.

🤖

Data Scientist

Apply probabilistic and statistical modelling skills to large datasets at technology companies and consultancies.

🧮

Insurance Mathematician

Model policyholder risk, design premium structures, and develop loss reserving models for insurance companies.

💹

Quantitative Analyst

Develop mathematical models for derivatives pricing, portfolio optimisation, and algorithmic trading strategies.

Top Universities Offering This Programme
London School of Economics University of Warwick University of Edinburgh University of Bristol University of Bath University of Toronto University of Auckland Monash University University of Copenhagen University of Hong Kong

Why D'Math University

01

Dual-Discipline Depth

Uniquely combining rigorous probability theory with powerful applied statistics — the strongest foundation for actuarial, finance, and data careers.

02

Four Specialist Tracks

Actuarial, Financial, Computational, and Applied tracks let you shape your degree around your career goals from Year 2.

03

IFoA-Aligned Modules

Actuarial probability and statistics modules are designed to provide maximum exemptions from IFoA CT-series examinations.

04

MSc Progression

Strong academic performers receive guaranteed entry to our MSc Statistics, MSc Biostatistics, or MSc Data Science programmes.

Enrol in BSc Probability & Statistics →

Flexible start dates — choose your track at the end of Year 1