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Back to the lesson libraryMECHANISM · 12 MIN
M06.6 CONNECT THE MECHANISM

Estimate a difficult average by sampling

Throw random darts at a square and you can find π. Learn why that works, why 100 times more darts only buys 10 times more accuracy, and how a random walk samples the unsampleable.

LESSON OVERVIEW12 min lesson

Lesson overview

Throw random darts at a square and you can find π. Learn why that works, why 100 times more darts only buys 10 times more accuracy, and how a random walk samples the unsampleable.

What you’ll explore

  • Monte Carlo approximates expectations with samples; Markov-chain methods target difficult distributions, but dependence, mixing, and diagnostics limit the effective evidence.
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Original explanations, connected to the research.

Deep Learning — probability and information theoryArtificial Intelligence: A Modern Approach — authors’ materialsEquation of State Calculations by Fast Computing Machines (Metropolis et al., 1953)
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