Home › Previous year questions › GATE 2022 MN › Question 15GATE 2022 MN – Question 15 Mineral Economics, Mine Planning, Systems Engineering · Mine Planning · 1 mark · Multiple choice
A deposit has grade X in [0, 30] with probability density f(x). At cutoff grade $x_c$, what proportion is ore?
$\int_0^{30}f(x)dx-\int_0^{x_c}f(x)dx$ $\frac12\int_0^{30}f(x)dx-\int_0^{x_c}f(x)dx$ $\frac12\int_0^{30}f(x)dx+\int_0^{x_c}f(x)dx$ $\int_0^{x_c}f(x)dx$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) $\int_0^{30}f(x)dx-\int_0^{x_c}f(x)dx$
Explanation Ore has grade at least the cutoff, so its proportion is $P(X\ge x_c)=\int_{x_c}^{30}f(x)dx$. Splitting the full integral at the cutoff gives A. The integral below the cutoff alone is the waste proportion; the density has total integral one.
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