An electric component is known to have a length of life defined by an exponential density with failure rate $10^{-7}$ failures per hour. Determine the fraction of those components that will fail before the mean or expected life? Can you please help me, how should I answer this?
2026-03-27 10:06:56.1774606016
Exponential distribution with failure rate
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For any exponential distribution, the fraction of components failing in less than the mean lifetime is the same,$$\int_0^{1/\lambda}\lambda e^{-\lambda x}dx=1-\frac1e.$$For what it's worth, $\lambda$ is simply the mean failure rate.