Hw2_solution_to_POST - a. For what values of p will P(G | R...

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Fall 2007 Supplemental exercises (p. 94)u # 106abcd (Devore 6 th edition - #104abcd) a. P(G | R 1 < R 2 < R 3 ) = 67 . 075 . 15 . 15 . = + > .5 => classify as granite P(B | R 1 < R 2 < R 3 ) = .33 < 0.5 b. P(G | R 1 < R 3 < R 2 ) = 2941 . 15 . 0625 . 0625 . = + < .5 => classify as basalt. P(G | R 3 < R 1 < R 2 ) = 0667 . 5625 . 0375 . = < 0.5 => classify as basalt. c. P(erroneous classif) = P(B classif as G) + P(G classif as B) = P(classif as G | B)P(B) + P(classif as B | G)P(G) = P(R 1 < R 2 < R 3 | B)(.75) + P(R 1 < R 3 < R 2 or R 3 < R 1 < R 2 | G)(.25) = (.10)(.75) + (.25 + .15)(.25) = .175
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Unformatted text preview: a. For what values of p will P(G | R 1 &lt;R 2 &lt;R 3 ) &gt; .5, P(G | R 1 &lt; R 3 &lt; R 2 ) &gt; .5, and P(G | R 3 &lt; R 1 &lt; R 2 ) &gt; .5? P(G | R 1 &lt; R 2 &lt; R 3 ) = 5 . 5 . 1 . 6 . ) 1 ( 1 . 6 . 6 . + =-+ p p p p p if 7 1 p P(G | R 1 &lt; R 3 &lt; R 2 ) = 5 . ) 1 ( 2 . 25 . 25 .-+ p p p if 9 4 p P(G | R 3 &lt; R 1 &lt; R 2 ) = 5 . ) 1 ( 7 . 15 . 15 .-+ p p p iff 17 14 p (most restrictive) If 17 14 p always classify as granite. 1...
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