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Lecture 6: Monte Carlo Simulation - MIT OpenCourseWare

Lecture 6: Monte Carlo Simulation Lecture 6 1 Relevant Reading Sections 15-1 Chapter 16 Lecture 6 2 A Little History Ulam, recovering from an illness, was playing a lot ofsolitaire Tried to figure out probability of winning, and failed Thought about playing lots of hands and countingnumber of wins, but decided it would take years Asked Von Neumann if he could build a program tosimulate many hands on Lecture 6 3 Image of ENIAC programmers contentis excluded from our Creative Commons license. For moreinformation,see Monte Carlo Simulation A method of estimating the value of an unknown quantity using the principles of inferential statistics Inferential statistics Population: a set of examples Sample: a proper subset of a population Key fact: a random sample tends to exhibit the same properties as the population from which it is drawn Exactly what we did with random walks Lecture 6 4 An example Given a single coin, estimate fraction of heads you would get if you flipped the coin an infinite number of times Consider one flip How confident would you be about answering Lecture 6 5 Flipping a Coin Twice Do you think that the next flip will come up heads?

Monte Carlo Simulation A method of estimating the value of an unknown quantity using the principles of inferential statistics Inferential statistics Population: a set of examples Sample: a proper subset of a population Key fact: a . random sample . tends to exhibit the same properties as the population from which it is drawn

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