These days, I want to calculate the probability below: $$P\left(x_6-x_5\le\mathop{\mathop{max}\limits_{1\le i,j\le4}}\limits_{i\neq j}(|x_i-x_j|)\right)$$ $$x_i\mathop{\sim}^{iid}N(0,\sigma^2),i=1\sim 6$$ I obtain $P=0.89$ by software simulation and the probability is irrelevant with the $\sigma^2$. So how to calculate the probability?
2026-04-03 09:24:03.1775208243
conditional Probability of a Normal Distribution?
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