Monte Carlo Estimation Examples with Matlab

A set of examples of Monte Carlo numerical estimation methods.

The Matlab codes presented here are a set of examples of Monte Carlo numerical estimation methods (simulations) – a class of computational algorithms that rely on repeated random sampling or simulation of random variables to obtain numerical results.

Twelve examples are given:

MonteCarloCoin1.m – estimation of the probability of obtaining 8 or more heads, if a coin is tossed 10 times;

MonteCarloCoin2.m – estimation of the probability of obtaining 3 consecutive heads, if a coin is tossed 3 times;

MonteCarloDice.m – estimation of the probability of obtaining 6 & 6, if two dice are flipped;

MonteCarloIntegration.m – estimation of the integral of abs(sin(x)), for x = 0 .. 2pi;

MonteCarloPi.m – estimation of the Pi value;

MonteCarloPoker1 - estimation of the probability of getting “Four of a Kind” when 5 cards are dealt;

MonteCarloPoker2 - estimation of the probability of getting “Full House” when 5 cards are dealt;

MonteCarloPower.m – estimation of the worst-case resistor's power dissipation;

MonteCarloSqrt2.m – estimation of the sqrt(2) value;

MonteCarloSysEq.m – solve a system of equations using Monte Carlo algorithm;

MonteCarloVol.m – estimation of the unit sphere volume;

MonteCarloVol_visualization.m – a visualization of the MonteCarloVol.m example.

The codes are based on the theory described in:

[1] I. Sobol. A primer for the Monte Carlo method. Boca Raton, CRC Press, 1994.