课程: Probability Foundations for Data Science

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Monte Carlo Approximation

Monte Carlo Approximation

- Let's explore Monte Carlo approximations. Monte Carlo approximation is a technique that uses random sampling to estimate mathematical quantities that might be difficult or impossible to solve analytically by providing a probabilistic interpretation. The reason why Monte Carlo approximation relies on random sampling of probability distributions is to explore the space of possible outcomes. Monte Carlo approximation relies on random sampling to estimate mathematical quantities such as integrals, expectations, or solutions to complex systems. By calculating the outcomes of these random samples, you can estimate the desired quantity in a probabilistic way. So how is the law of large numbers related to Monte Carlo approximations? Remember, with the law of large numbers, the average of a large numbers of independent and identically distributed random samples will converge to the expected value. In Monte Carlo approximation, each random sample represents a possible outcome and their…

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