Monte Carlo simulation is a technique that uses random numbers and random variates to solve stochastic or deterministic problems that do not involve the passage of time. It is used to evaluate integrals of functions that cannot be directly integrated. The method involves defining a random variable equal to the function multiplied by the interval length and taking the sample mean of this random variable from running multiple simulations, which converges to the true expected value and integral.

1. Monte Carlo Simulation Adapted From Law and Kelton

4. To use simulation, let Y be that random variable (b-a)g(X), where X is a continuous random variable distributed uniformly on [a,b]. Thus, = I

5. But, E(Y) can be estimated using the concept of the sample mean . Thus,

6. Ex. Evaluate (Answer is 2). n 10 20 40 80 160 2.213 1.951 1.948 1.989 1.993