General 
Syllabus 

Homeworks and Exams 
Some Basic Ideas and Concepts 
Introduction to ESMA 5015 
R 
An Introduction to R 

R Programing Language and UserWritten Functions 

Extending R 

Some R Commands 
Simulation 
An Example: Monopoly 
Probability 
Introduction 

Conditional Probability and Independence 

Random Variables and Random Vectors 

Expectation of a R.V. 

Functions of a R.V.  Transformations 

Inequalities and Limit Theorems 
Some Standard Distributions 
Discrete Distributions 

Continuous Distributions 
Generating Random Variables 
General Methods 

Fundamental Theorem of Simulation 

Special Cases 
Statistics 
Basic Statistics 

Verifying the Simulation 

A Realistic Example 
Stochastic Processes 
Discrete  Time Markov Chains 

MCMC  Markov Chain Monte Carlo 

The Gibbs Sampler 

The Slice Sampler 

Bayesian Inference for Normal Distribution 
Variance Reduction Methods 
Antithetic and Control Variables 

Conditioning and Importance Sampling 
Stochastic Optimization 
Stochastic Optimization and Simulated Annealing 

The EM Algorithm 
Larger Simulations 
The Symmetric Random Walk in R^{d} 

Random Walk  Routines and Data 

Estimating the Waiting Time 

Risk! 