Mathematics, 11.02.2020 17:26 Arealbot
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last more than 1,200 hours?
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![P(X1200)=1-P(X\leq 1200)\\=1-\int\limits^{1200}_{0} {\lambda e^{-\lambda x}} \, dx \\=1-\lambda[\frac{e^{-\lambda x}}{-\lambda} ]^{1200}_{0}\\=1-[1-e^{-\frac{x}{1000} }]^{1200}_{0}\\=1-[1-e^{-\frac{1200}{1000}}]\\=e^{-1.2}\\=0.3012](/tpl/images/0506/6269/7ba3b.png)
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The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probab...
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