probability gamma distribution

logistic_guy

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Joined
Apr 17, 2024
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here is the question

For an electrical component with a failure rate of once every \(\displaystyle 5\) hours, it is important to consider the time that it takes for \(\displaystyle 2\) components to fail.

(a) Assuming that the gamma distribution applies, what is the mean time that it takes for \(\displaystyle 2\) components to fail?
(b) What is the probability that \(\displaystyle 12\) hours will elapse before \(\displaystyle 2\) components fail?


my attemv
the PDF of gamma distribution \(\displaystyle f(x) = \frac{x^{\alpha - 1}}{\Gamma(\alpha)\beta^{\alpha}}e^{-\frac{x}{\beta}}\)
the mean \(\displaystyle \alpha \beta\)
how to tell what's \(\displaystyle \alpha\) and \(\displaystyle \beta\) from the question?
it's also confusing for (b)☹️
do the probability \(\displaystyle P(X > 12)\) or \(\displaystyle P(X < 12)\)
it's confusing🥺
 
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