Let T denote the time it takes for a computer to shut down. Suppose T follows an Exponential distribution with mean 10 seconds A computer lab has 10 independent computers that must all be shut down at the end of the day.

a) What is the probability that it takes any given computer at least 10 seconds to shut down?

b) What is the probability that it takes any given computer at least 1 minute to shut down?

c) What is the probability that all 10 computers successfully shut down in under a minute?

Question

Bruce Hogan

Mathematics

19 April, 04:33

Let T denote the time it takes for a computer to shut down. Suppose T follows an Exponential distribution with mean 10 seconds A computer lab has 10 independent computers that must all be shut down at the end of the day.

a) What is the probability that it takes any given computer at least 10 seconds to shut down?

b) What is the probability that it takes any given computer at least 1 minute to shut down?

c) What is the probability that all 10 computers successfully shut down in under a minute?

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Answers (1)

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Schaefer · Answer 1

P (T > 1) = e ^ ( - 1/10) = e ^ ( - 0.1) ≈ 2.71828.

Let X denote the number of computers (out of 10) that take longer than 10 secs. to

shut down. Then X has a Binomial distribution, n = 10, p = e ^ (-0.1) = 2.71828.

(a)

P (X ≤ 1) = 10 C 0 (e ^ (-0.1)) ^ 0 (1 - e ^ ( - 0.1) ^10

(b)

P (X ≤ 1) = 10 C 0 (e ^ (-1/1)) ^ 0 (1 - e ^ (-1/1) ^10

(c)

P (X ≤ 10) = 10 C 0 (e ^ (-0.1)) ^ 0 (1 - e ^ ( - 0.1) ^10