Probabilistic analysis of transportation systems: Axioms and principles, probability density and mass function, cumulative distribution functions, and common distributions; probabilistic modelling of demand, supply, loading, headways and arrivals in transportation systems, statistical characterisation of means, variance, distributions, and moments of performance functions (travel time, distance, speed, waiting times etc.); applications to traffic flow, transit operations, urban travel services, passenger characteristics, freight travel analysis. Statistical models and Transportation Applications: Sampling and Hypothesis testing (for means and variances), consistency, bias, power, and efficiency in statistical models; linear models – linear regression, analysis of variance, applications in trip generation, demand, and travel quantification; introduction to discrete choice modelsbinary, multinomial logit, and ordered frequency models applied to disaggregate travel choice analysis. Optimisation Techniques: Basic concepts; linear programming – simplex method, duality and applications to minimum cost and transportation problems; Formulation of transportation problems as mathematical programs (scheduling, routing, distribution, faculty location, network equilibrium, network design, crew scheduling etc.)