logistic_guy
Full Member
- Joined
- Apr 17, 2024
- Messages
- 424
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
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