Given the continuous uniform distribution $U(a,b)$ and any 2 values $u_1,u_2$ picked from $U$, what are the odds that $u_1 > u_2$?
2026-04-01 13:09:04.1775048944
What are the odds that one value picked from a uniform distribution is greater than any other?
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By symmetry, the probability that $u_1\gt u_2$ is equal to the probability that $u_2\gt u_1$. Since the distribution is continuous, $u_1\ne u_2$. Therefore, the probability that $u_1\gt u_2=\frac{1}{2}$.