GATE 2014 EC (EC3) – Question 39
X₁,X₂,X₃ are independent identically distributed uniform variables on [0,1]. Find P{X₁ + X₂ ≤ X₃}.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.15 to 0.18
Explanation
Condition on X3=z in[0,1]. In the unit square for(X1,X2), the event x1+x2≤z is a triangle of area z²/2. Average over the uniform z:∫₀¹z²/2dz=**1/6≈0.166667**. Independence makes the joint density1on the unit cube.