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A fault-tolerant system that processes transactions for nancial services rm uses three separate computers. If operating...

A fault-tolerant system that processes transactions for nancial services rm uses three separate computers. If operating computer fails, one of the two spares can be immediately switched online. After the second computer fails, the last computer can be immediately switched online. Assume that the probability of a failure during any transaction is 10?8 and that the transctions can be considered to be independent events. (a) What is the mean number of transactions before all computers have failed? (b) What is the probability that at least 10 transctions were done before the all computers failed?

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Answer #1

Ans:

Use negative binomial distribution with r=3 and p=10^-8

a)

mean=r/p=3/10^-8=3*10^8

b)

P(x>=10)=1-P(x<=9)=1-NEGBINOM.DIST(7,3,10^-3,TRUE)=1.0000

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