An electrical component has a time to failure (or lifetime) distribution that is exponential with parameter lambda , so the mean lifetime is mu 1 lambda Suppose that a sample of n of these components is put on test, and let Xi be the observed lifetime of component i The test continues only until th...

a PX3 2T X1 P 21 21 Then a confidence ...

An electrical component has a time-to-failure (or lifetime) distribution that is exponential with parameter λ, so the

Question:

An electrical component has a time-to-failure (or lifetime) that is exponential with parameter λ, so the mean lifetime is μ = 1/λ. Suppose that a sample of n of these components is put on test, and let Xi be the observed lifetime of component i. The test continues only until the rth unit fails, where r

We have previously shown in Exercise 7-72 that Tr/r is an unbiased estimator for μ.
(a) It can be shown that 2λTr has a chi-square with 2r degrees of freedom. Use this fact to develop a 100(1 €“ a) % confidence interval for mean lifetime μ = 1/λ.
(b) Suppose 20 units were put on test, and the test terminated after 10 failures occurred. The failure times (in hours) are 15, 18, 19, 20, 21, 21, 22, 27, 28, 29. Find a 95% confidence interval on mean lifetime.
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...