b What proportion of the machines do you think will fail bef

(b) What proportion of the machines do you think will fail before 1000 hours?

The time between failures of a machine has an exponential distribution with parameter lambda . (b) What proportion of the machines do you think will fail before 1000 hours? bar{x}=1223 hours. (a) Find 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