hw1solu

# Hw1solu - HW 1 Solutions 2.3 a Event A = cfw SSF SFS FSS b Event B = cfw SSS SSF SFS FSS c For Event C the system must have component 1 working S

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HW 1: Solutions 2.3. a. Event A = { SSF, SFS, FSS } b. Event B = { SSS, SSF, SFS, FSS } c. For Event C, the system must have component 1 working ( S in the first position), then at least one of the other two components must work (at least one S in the 2 nd and 3 rd positions: Event C = { SSS, SSF, SFS } d. Event C = { SFF, FSS, FSF, FFS, FFF } Event A C = { SSS, SSF, SFS, FSS } Event A C = { SSF, SFS } Event B C = { SSS, SSF, SFS, FSS } Event B C = { SSS SSF, SFS } 2.13. a. awarded either #1 or #2 (or both): P(A 1 A 2 ) = P(A 1 ) + P(A 2 ) - P(A 1 A 2 ) = .22 + .25 - .11 = .36 b. awarded neither #1 or #2: P(A 1 A 2 ) = P[(A 1 A 2 ) ] = 1 - P(A 1 A 2 ) = 1 - .36 = .64 f. either (neither #1 nor #2) or #3: P[( A 1 A 2 ) A 3 ] = P(awarded none) + P(A 3 ) = .47 + .28 = .75 2.22 a. P(A 1 A 2 ) = P(A 1 ) + P(A 2 ) - P(A 1 A 2 ) = .4 + .5 - .6 = .3 b. P(A 1 A 2 ) = P(A 1 ) - P(A 1 A 2 ) = .4 - .3 = .1 c. P(exactly one) = P(A

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## This note was uploaded on 03/22/2011 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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Hw1solu - HW 1 Solutions 2.3 a Event A = cfw SSF SFS FSS b Event B = cfw SSS SSF SFS FSS c For Event C the system must have component 1 working S

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