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📅 May 3, 2026 👤 scraface

May 03, 2026

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Standard technique: Compute the complementary probability — that **no*...
Let $ X_1, X_2, \dots, X_6 \sim \text{Uniform}[0,10] $, and define $ X...
For all six points to lie within some interval of length 2, it is nece...
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...

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