Mathematics, 11.11.2020 17:50 chanel2013
A device runs until either of two comonents fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x, y) = x + y/8 for 0 < x < 2 and 0 < y < 2Calculate the probability that the device fails during its first hour of operation.
Answers: 2
![=1-\int\limits^{2}_{1} {\frac{x^{2}+2xy}{16}}|^{2}_{1} \, dy\\\\=1- \int\limits^{2}_{1}[{\frac{4+4y}{16}-\frac{1+2y}{16}}] \, dy\\\\=1-\int\limits^{2}_{1}{\frac{3+2y}{16}}\, dy\\\\=1-[\frac{3y+y^{2}}{16}]^{2}_{1}\\\\=1-0.375\\\\=0.625](/tpl/images/0887/9473/301c2.png)
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A device runs until either of two comonents fails, at which point the device stops running. The join...
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