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q02-f2008 - STA 4321/5325 Mathematical Statistics 1 Fall...

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STA 4321/5325 Quiz 2 Name: KEY Mathematical Statistics 1 Fall 2008 UF ID: 1. In responding to survey questions which concern sensitive topics people may not respond truthfully. Suppose that we plan to survey 12th graders and ask “Have you tried marijuana?” Assume that 40% of 12th graders who have tried marijuana will lie and respond “no”, and that 10% of those who have not tried marijuana will lie and respond “yes”. Assume also that 55% of all 12th graders have actually tried marijuana. A 12th grader is selected at random. (a) What is the probability that the person selected will answer “yes” to the question? (SET UP ONLY) (5 pts) M = { has tried marijuana } Y = { answers yes } N = { answers no } = Y P ( N | M ) = . 40 = P ( Y | M ) = . 60 P ( Y | M ) = . 10 P ( M ) = . 55 = P ( M ) = . 45 P ( Y ) = P ( M ) P ( Y | M ) + P ( M ) P ( Y | M ) = ( . 55)( . 60) + ( . 45)( . 10) = 0 . 375 (b) If the person selected answers “yes,” what is the probability that the person has actually tried marijuana? (SET UP ONLY) (5 pts) P ( M | Y ) = P ( M Y ) P ( Y ) = P ( M ) P ( Y | M ) P ( M ) P ( Y | M ) + P ( M ) P ( Y | M ) = ( . 55)( . 60) ( . 55)( . 60) + ( . 45)( . 10) = . 33 . 375 = . 88
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STA 4321/5325 Quiz 2 2 2. An electrical circuit is composed of relays of types A, B, and C in the configuration pic- tured below. Suppose that individual relays of types A, B, and C function properly with
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