MIT6_042JS10_lec38

# MIT6_042JS10_lec38 - Mathematics for Computer Science...

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1 Albert R Meyer, May 10, 2010 lec 14M.1 Mathematics for Computer Science MIT 6.042J/18.062J Sampling & Confidence Albert R Meyer, May 10, 2010 lec 14M.2 Estimate % contaminated fsh in Charles River? Procedure: catch n Fish, test each, use %contaminated in catch as estimate oF %contaminated in whole river Sampling Albert R Meyer, May 10, 2010 lec 14M.3 Sampling Questions Catch 500 fsh; what is probability that estimate is within 0.1 oF the actual Fraction? Albert R Meyer, May 10, 2010 Model as Coin Tosses lec 14M.4 p ::= Fraction contaminated in river test a Fish ± toss bias p coin catch n Fish ± toss n coins A n ::= Fraction contaminated in the sample oF n Albert R Meyer, May 10, 2010 Pr A n - μ > ± {} ² 1 n ³ ± ´ µ · ¸ ¹ 2 Pr A 500 - p > 0.1 {} ± 1 500 ² 0.1 ³ ´ µ · ¸ 2 Pairwise Independent Sampling 1/2 n = 500 , μ = p , ± = 0.1 worst ² = 1 2 Albert R Meyer, May 10, 2010 Pr A n - μ > ± {} ² 1 n ³ ± ´ µ · ¸ ¹ 2 Pr A 500 - p > 0.1 {} ± 1 500 ² 0.1 ³ ´ µ · ¸ 2 Pairwise Independent Sampling 1/2 Pr A 500 -p ± 0.1 {} > 0.95 n = 500 , = p , = 0.1

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2 Albert R Meyer,
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MIT6_042JS10_lec38 - Mathematics for Computer Science...

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