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Monte Carlo Methods
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== <span style="color: #FFFFFF;">Remembering</span> == * '''Monte Carlo Method''' β A broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. * '''Stanislaw Ulam''' β The mathematician who invented the method while playing "Solitaire" in a hospital bed. * '''Random Sampling''' β The act of picking a "Random data point" to see what happens. * '''Convergence''' β The idea that as you run "More and More" simulations, the average result gets "Closer and Closer" to the "True" answer. * '''The Law of Large Numbers''' β The mathematical rule that says the average of a large number of trials will be close to the expected value. * '''Markov Chain Monte Carlo (MCMC)''' β A complex version that "Wanders" through a problem space to find the most likely answers. * '''Confidence Interval''' β The "Range of certainty" in a Monte Carlo result (e.g., "The answer is 42, with a 95% chance it's between 41 and 43"). * '''Pseudorandom Number Generator (PRNG)''' β The computer "Brain" that generates the "Fake" random numbers used in the simulations. * '''Integration''' β Using Monte Carlo to find the "Area" of a weird shape by "Throwing random darts" at it. * '''Sensitivity Analysis''' β Using Monte Carlo to see "Which variable" (e.g., Oil Price vs. Interest Rate) has the biggest effect on a project. </div> <div style="background-color: #006400; color: #FFFFFF; padding: 20px; border-radius: 8px; margin-bottom: 15px;">
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