The time between failures of a machine has an exponential distribution with parameter Suppose that the prior distribution for is exponential with mean 100 hours Two machines are observed, and the average time between failures is x 1125 hours (a) Find the Bayes estimate for (b) What proportion of th...

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The time between failures of a machine has an exponential distribution with parameter . Suppose that the

Question:

The time between failures of a machine has an exponential distribution with parameter λ. Suppose that the prior distribution for λ is exponential with mean 100 hours. Two machines are observed, and the average time between failures is x̅ = 1125 hours.

(a) Find the Bayes estimate for λ.

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

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

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