pfinal - Solutions to practice final Pstat 120A,UC Santa...

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Unformatted text preview: Solutions to practice final Pstat 120A ,UC Santa Barbara Problem 1 M: Malaria, H: Headache P ( M ) = 0 . 01 P ( H | M c ) = . 05 P ( H | M ) = 0 . 8 P ( M | H ) = P ( MH ) P ( H ) = P ( H | M ) P ( M ) P ( H | M ) P ( M ) + P ( H | M c ) P ( M c ) = 8 8 + 5 * 9 . 9 = . 1391 Problem 2 Let B i denote the event draw Blue in i th and R i denote Red in i th draw. Where i = 1 , ··· , 5. To find P ( X = k ) for k = 1 , ··· , 4. P ( X = 1) = P ( B 1 , B 2 , B 3 ) = P ( B 3 | B 2 , B 1 ) P ( B 2 | B 1 ) P ( B 1 ) = 3 4 . 2 3 . 1 2 = 1 4 P ( X = 2) = P ( R 1 , B 2 , B 3 ) + P ( B 1 , R 2 , B 3 ) + P ( B 1 , B 2 , R 3 ) = P ( B 3 | B 2 , R 1 ) P ( B 2 | R 1 ) P ( R 1 ) + P ( B 3 | R 2 , B 1 ) P ( R 2 | B 1 ) P ( B 1 ) + P ( R 3 | B 2 , B 1 ) P ( B 2 | B 1 ) P ( B 1 ) = 2 4 . 1 3 . 1 2 + 2 4 . 1 3 . 1 2 + 1 4 . 2 3 . 1 2 = 1 4 . We can similarly show P ( X = 3) = P ( X = 4) = 1 4 1 Problem 3 ( a ) P ( X ≤ 1 / 2) = F (1 / 2) = 3 / 4 ( b ) P ( X = 1 / 2) = P ( X ≤ 1 / 2)- P ( X < 1 / 2) = 3...
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This note was uploaded on 04/21/2009 for the course STAT 120A taught by Professor Englander during the Spring '09 term at UCSB.

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pfinal - Solutions to practice final Pstat 120A,UC Santa...

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