GATE 2014 EC (EC1) – Question 15
X₁,X₂,X₃ are independent identically distributed uniform random variables on [0,1]. Find P{X₁ is the largest}.
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Correct answer: 0.32 to 0.34
Explanation
The variables are independent and identically distributed with a continuous distribution, so ties have probability zero. By symmetry each variable has the same probability of being the unique maximum. These three disjoint events exhaust probability1, giving **P(X1 largest)=1/3**.