What proportion of the machines do you think will fail befo

- What proportion of the machines do you think will fail before 1000 hours? (round the answer to three decimal places)

The time between failures of a machine has an exponential distribution with parameter Lambda is 0.00123 - What proportion of the machines do you think will fail before 1000 hours? (round the answer to three decimal places) x = 1223 hours.- the Bayes estimate for Lambda is exponential with mean 100 hours. Two machines are observed, and the average time between failures is Lambda . Suppose that the prior distribution for

Solution

Bayes estimate for lemda the difference between two failures = x bar/Mean^4 = 1223/1000000

=0.001223 (apprxmly)

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As lemda = 0.001223

P(X<1000) = 1-e^{-0.001223(1000)}

= 1-e^-0.1223

= 0.0909