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? (round the answer to three decimal places)

The time between failures of a machine has an exponential distribution with parameter lambda .(round the answer to five decimal places) (b) What proportion of the machines do you think will fail before 1000 hours? (round the answer to three decimal places) 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)

---------------------------------------------------

As lemda = 0.001223

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

= 1-e^-0.1223

= 0.0909