What is Monte Carlo Simulation? Write in brief about the Monte Carlo Simulation Procedure.
Monte Carlo Simulation is a computational technique that uses random sampling and probability distributions to model and simulate complex systems or processes. It is named after the famous casino in Monte Carlo, known for its games of chance.
In the Monte Carlo Simulation procedure, the first step involves defining the problem or system to be analyzed and developing a mathematical model. This model should include the variables, assumptions, and relationships between different components of the system.
Next, probability distributions are assigned to the input variables of the model. These distributions represent the uncertainty or variability associated with each input. Common distributions used are normal (Gaussian), uniform, and triangular distributions.
Multiple random samples are generated from the input variable distributions using random number generators or sampling techniques. These samples are known as iterations or trials. Each iteration represents a set of values for the input variables, which are used to calculate the output or results of the model.
For each iteration, the model is run, and the output or results are recorded. This process is repeated numerous times to generate a large sample size, ensuring a more accurate representation of the system's behavior.
After running a sufficient number of iterations, the collected output data is analyzed to determine the statistical properties of the system. This includes calculating summary statistics such as mean, standard deviation, percentiles, and confidence intervals. The distribution of the output data provides insights into the uncertainty and risk associated with the system.
Monte Carlo Simulation can be used in various fields, including finance, engineering, manufacturing, healthcare, and project management. It enables decision-makers to explore different scenarios, evaluate risk, make informed decisions, and optimize system performance by considering the range of possible outcomes and their associated probabilities.