The Monte Carlo method estimates the expected value by replacing difficult analytical integrals with the average of random samples. It draws independent random samples from the target distribution, computes their running average, and observes the average converging to the true expected value as the number of samples increases.
Conditions: Requires the ability to draw random samples from the target distribution.; Accuracy improves as the number of samples increases.; must be a valid probability density function.
The Monte Carlo method estimates the expected value by replacing difficult analytical integrals with the average of random samples. It draws independent random samples from the target distribution, computes their running average, and observes the average converging to the true expected value as the number of samples increases.
Conditions: Requires the ability to draw random samples from the target distribution.; Accuracy improves as the number of samples increases.; must be a valid probability density function.