MIT2_854F10_MonteCarlo

MIT2_854F10_MonteCarlo - • Probability Estimation Through...

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Unformatted text preview: • Probability Estimation Through the Indicator Function • System Reliability Example With Crystal Ball • Same Seed to Compare Alternatives • Modeling Correlation Between Random Numbers • Option Pricing using Crystal Ball Probability Estimation Through E[I A ] Problem Estimate the probability of event A happening. Method Define an Indicator function I A as the following I A = 1 if event A occurs and 0 otherwise P( A occurs) = E[I A ] Probability Estimation Through E[I A ] Proof : P( A occurs) = E[I A ] since, E[I A ] = 1 * P( A occurs) + 0 * P(A doesn’t occur) = P( A occurs) Recitation • Probability Estimation Through the Indicator Function • System Reliability Example With Crystal Ball • Same Seed to Compare Alternatives • Modeling Correlation Between Random Numbers • Option Pricing using Crystal Ball System Reliability Example A C D B System Reliability Example A C D B Reliability of 90% System Reliability Example A C D B Reliability of 90% Reliability of 85% System Reliability Example A C D B System fails when either 1. A fails, or 2. B, C, and D fail together 3. or both System Reliability Example A C D B See Excel file: Component Failure.xls Recitation...
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.854 taught by Professor Stanleygershwin during the Fall '10 term at MIT.

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MIT2_854F10_MonteCarlo - • Probability Estimation Through...

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