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Home » The ratio of the volume of the sphere to the volume of the hemisphere is: - AMAZONAWS

The ratio of the volume of the sphere to the volume of the hemisphere is: - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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X_{(6)} - X_{(1)} \leq 2
Because then the earliest and latest arrivals are within 2 minutes, an...
Now, we compute:
P(X_{(6)} - X_{(1)} \leq 2) \quad \text{for } X_i \sim \text{Uniform}[...
Scale: Let $ Y_i = X_i / 10 \sim \text{Uniform}[0,1] $. Then $ Y_{(1)}...
The joint distribution of $ (Y_{(1)}, Y_{(6)}) $ has joint density:
f_{Y_{(1)}, Y_{(6)}}(u,v) = 6 \cdot 5 \cdot (v - u)^{4}, \quad 0 \leq...
P(Y_{(6)} - Y_{(1)} \leq 0.2) = \int_{u=0}^1 \int_{v=u}^{u+0.2} 30(v -...
Change variable: let $ s = v - u $, so $ v = u + s $, $ 0 \leq s \leq...
But since $ u \leq 1 - s \leq 1 $, and $ s \leq 0.2 $, the upper limit...

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