Preparation for Test 1 -solutions - Preparation to test 1...

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Unformatted text preview: Preparation to test 1 Solutions #1 Binomial Distribution A stick with tour group P(A) = 0,27 B own experience P(B) = 0,73 a) B success N=5 P=0,73 F(x3) - ? F(x3) = 1- F(x>3) = 1 F(x=4) F(x=5) = 1 0,383 0,207 = 0,41 k n k k n p p C k x f-- = = ) 1 ( ) ( )! ( ! ! k n k n C k n- = 5! F(x=4) = 4!1! * 4 ) 73 , ( * 1 ) 27 , ( = 0,383 5! F(x=5) = 5!0! * 5 ) 73 , ( * ) 27 , ( = 0,207 b) N=4 P=0,27 A success F(x 2) -? F(x 2) = 1-F(x<2) = 1- F(x=0)- f(x=1)= 1-0,283-0,420= 0,297 k n k k n p p C k x f-- = = ) 1 ( ) ( )! ( ! ! k n k n C k n- = 4! F(x=0)= 0! 4! * ) 27 , ( * 4 ) 73 , ( =0,283 4! F(x=1)= 1!3! * 1 ) 27 , ( * 3 ) 73 , ( = 0,42 #2 Binomial Distribution A system will detect attack P(A)= 0,85 a) n=4 (four system operates independently) we are asked about probability that at least two of the systems will not detect the attack therefore P=1-0,85 = 0,15 F(x 2) - ? F(x 2) = 1 f(x<2) = 1- f(x=0) f(x=1) = 1-0,522-0,368 = 0,11 F(x=0) = k n k k n p p C-- ) 1 ( = 4 C 4 ) 85 , ( ) 15 , ( = ! 4 ! ! 4 4 ) 85 , ( 1 =0,522 F(x=1) = k n k k n p p C-- ) 1 ( = 1 4 C 3 1 ) 85 , ( ) 15 , ( = ! 3 ! 1 ! 4 3 ) 85 , ( 15 , = 0,368...
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This note was uploaded on 03/11/2012 for the course FIN FIN 3230 taught by Professor Petrivanov during the Spring '12 term at Kazakhstan Institute of Management, Economics and Strategic Research.

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Preparation for Test 1 -solutions - Preparation to test 1...

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