Mathematics, 11.02.2020 17:57 mem8163
Suppose that the lifetime of a particular component has an exponential distribution with mean value 1000h.
(a) What is the probability that the lifetime is at most 2000h?
(b) What is the probability that the lifetime is more than 1000h?
(c) What is the probability that the lifetime is between 500h and 2000h?
(d) Compute the variance of the distribution?
Answers: 2
![P(X\leq 2000)=\int\limits^{2000}_{0} {\lambda e^{-\lambda x}} \, dx \\=\lambda[\frac{e^{-\lambda x}}{-\lambda} ]^{2000}_{0} \\=[-e^{\frac{-2000}{1000}}+e^{\frac{-0}{1000} } }]\\=1-0.1353\\=0.8647](/tpl/images/0506/6508/92046.png)
![P(X1000)=\int\limits^{\infty}_{1000} {\lambda e^{-\lambda x}} \, dx \\=\lambda[\frac{e^{-\lambda x}}{-\lambda} ]^{\infty}_{1000} \\=[-e^{\frac{-\infty}{1000}}+e^{\frac{-1000}{1000} } }]\\=0+0.3679\\=0.3679](/tpl/images/0506/6508/57d55.png)
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