HWKsolutions3lastsemester

50510049050511049037995 o

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Unformatted text preview: = 0 , D_2 = 1) ) = 2 * P( (D_1 = 1 , D_2 = 0) ) = note: symmetric = 2 * [ P( D_1 = 1) * P(D_2 = 0) ]= note: Independence of Child 1 and Child 2 = 2 * [ P(D_1 = 1 | C_1 = M) P(C_1 = M) + P(D_1 = 1 | C_1 = F)P(C_1 = F) ] * * [ P(D_2 = 0 | C_2 = M) P(C_2 = M) + P(D_2 = 0 | C_2 = F)P(C_2 = F) ] note: condition on M/F = 2 * [ (0.5)(0.51) + (0)(0.49) ] * [ (0.5)(0.51) + (1)(0.49) ] = 0.37995 o What is the probability that neither sibling is affected? ANS) Neither siblings affected { (D_1 = 0, D_2 = 0) } 1 http://www.stat.ucla.edu/%7Edinov/courses_students.dir/12/Winter/STAT13.1.dir/HWs.dir/HW03.html P ( D_1 = 0 and D_2 = 0 ) = P(D_1=0) * P(D_2=0) = P(D_1=0) ^2 = note: independence = P(D_1=0) = [ P(D_1=0|C_1=M)*P(C_1=M) + P(D_1=0|C_1=F)*P(C_1=F) ] ^2 = cond. on M/F = [ (0.5)(0.51) + (1)(0.49) ] ^2 = 0.5550525. (HW3.2) Suppose that a medical test has a 82% chance of detecting a disease if the person has it (i.e., 82% sensitivity) and a 91% chance of correctly indicating that the disease is absent if the person rea...
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