Let $X_1,X_2,X_3$ be three independent and mutually identically distributed random variabe with uniform distribution on [0,1]. What is the probability $P\{X_1 \rm{~is ~largest}\}$?
2026-03-27 10:09:05.1774606145
What is the probability $P\{X_1 \rm{~is ~largest}\}$?
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The probability is $\frac{1}{3}$. This follows from the fact that the probability that two of the variables are the same is 0. Due to the symmetrical situation, the probabilies, that $X_1$ , $X_2$ and $X_3$ is the greatest are equal.