Monte Carlo Methods and Simulation Random Variables Estimati

Monte Carlo Methods and Simulation Random Variables Estimation of Areas and Volumes by Monte Carlo Techniques Simulation

Solution

Monte-Carlo simulation with random variables

Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. The technique is used by professionals in such widely disparate fields such as finance, project management, energy, manufacturing, engineering, research and development, oil & gas, transportation etc.

Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.

By using probability distributions, variables can have different probabilities of different outcomes occurring. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis.

Estimation of areas and volumes by Monte Carlo method

Monte Carlo Integration which is used to estimate the value of an integral

.Take the function value at random points in the given range.

.The area (volume) times the average function value estimates the integral.

.To find or estimating the mean value of the function

.Multiplying it by the volume.