409Hw13ans - STAT 409 Fall 2009 Homework #13 (due Friday,...

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STAT 409 Homework #13 Fall 2009 (due Friday, December 4, by 4:00 p.m.) 1. Seventy percent of the light aircraft that disappear while in flight in Neverland are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft that has just disappeared has an emergency locator. What is the probability that it will not be discovered? P ( Discovered ) = 0.70, P ( Discovered ' ) = 1 - 0.70 = 0.30. P ( Locator Discovered ) = 0.60. P ( Locator ' Discovered ' ) = 0.90. Need P ( Discovered ' Locator ) = ? Locator Locator ' 0.60 0.70 Discovered 0.42 0.28 0.70 0.90 0.30 Discovered ' 0.03 0.27 0.30 0.45 0.55 1.00 P ( Discovered ' Locator ) = 15 1 = = 45 0 03 0 ) Locator P( ) Locator Discovered P( . . ' 0.06667 .
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In a certain industry sector, 40% of the stocks went up in January. Of the stocks that went up in January, 80% also went up in February. However, only 30% of the stocks that did not go up in January went up in February. J = { up in January }, F = { up in February }. P( J ) = 0.40. P( F | J ) = 0.80, P( F | J ' ) = 0.30. a) What is the probability that a randomly selected stock from this industry sector went up in February? F F ' Total J 0.40 0.80 0.32 0.08 0.40 J ' 0.60 0.30 0.18 0.42 0.60 Total 0.50 0.50 1.00 b) Suppose a stock from this industry sector went up in February. What is the probability that it also went up in January? P( J
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409Hw13ans - STAT 409 Fall 2009 Homework #13 (due Friday,...

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