MC - Introduction

1. A Monte Carlo method is a computational method that uses random numbers to compute (estimate) some quantity of interest 

2. MC two methods - independent samples of the random variable. This is usually called direct, simple or crude Monte Carlo. - Markov Chain Monte Carlo (MCMC) methods. These methods construct a Markov Chain whose stationary distribution is the probability measure we want to simulate. 

3. All Monte Carlo simulations require a source of randomness 

Examples Suppose we want to compute a definite integral over an interval like

  Let X be a random variable that is uniformly distributed on [a, b]. Then the expected 

value of f(X) is