Mathematics, 05.05.2020 21:07 chilanka
Explosive devices used in mining operations produce nearly circular craters when detonated. The radii of these craters are exponentially distributed with mean feet. Find the mean and variance of the areas produced by these explosive devices.
Answers: 2
![E(A)=E(\pi X^{2})\\=\pi\times E(X^{2})\\=\pi\times [V(X)+[E(X)]^{2}]\\=\pi\times [100+100]\\=200\pi](/tpl/images/0642/5523/ff3bb.png)
![V(A)=V(\pi X^{2})\\=\pi^{2}\times V(X^{2})\\=\pi^{2}\times [E(X^{4})-(E(X^{2}))^{2}]\\](/tpl/images/0642/5523/a4845.png)
![V(A)=\pi^{2}\times [E(X^{4})-(E(X^{2}))^{2}]\\=\pi^{2}\times [240000-200^{2}]\\=200000\pi^{2}](/tpl/images/0642/5523/fd07b.png)
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Explosive devices used in mining operations produce nearly circular craters when detonated. The radi...
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