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test 4 takehome sols

# test 4 takehome sols - Name Test#4 Integrals Take-home...

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Name: ______________ Test #4: Integrals Take-home portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death (BSOD) within the first t years given by the probability density function ( t > 0) f t = 4 t t 2 2 2 A. What's the probability that a computer will get its first BSOD between the 2 nd and 4 th year? 2 4 4 t t 2 2 2 dt = .222 Or 22.2% B. What's the probability that a 10 year old computer won't have gotten a BSOD? 1 0 10 4 t t 2 2 2 dt = .0196 Or about 2% C. By what time (exact, or rounded to the nearest hundredth) will half the computers get their first BSOD? We need to solve the pdf 0 d 2 2 t t 2 2 2 dt = .5 for d . Using u = t 2 2 and du = 2 t dt , we get: 2 t = 0 t = d 1 u 2 du = 2 u 1 t = 0 t = d = 2 1 t 2 2 0 d = 2 − 1 d 2 2 1 2 = 1 2 d 2 2 Setting this to .5, we get: 1 2 d

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