General 
Syllabus 

Homeworks and Exams 
Probability 
Fundamentals 

Basic Theorems 

Conditional Probability and Independence 

Combinatorics 

Random Variables 

Random Vectors 

Expectation and Covariance 

Functions of a R.V.  Transformations 
Some Standard Distributions 
Discrete Distributions 

Continuous Distributions 

Normal Distributions 
Inequalities and 
Inequalities 
Limit Theorems 
Limit Theorems 

Central Limit Theorems 

Law of the Iterated Logarithm 

Approximations 
Statistics 
Statistics 
Stochastic Processes 
Introduction 

Poisson Process 

Markov Chains 

Continuoustime Markov Chains 

Martingales 

Brownian Motion and Stationary Processes 
R 
An Introduction to R 

R Programing Language and UserWritten Functions 

Some R Commands 
Simulation 
General Methods 

Special Cases 

MCMC  Markov Chain Monte Carlo 

An Example 