GATE 2021 IN – Question 47
Independent continuous random variables have uniform distributions $X\sim U(2,3)$ and $Y\sim U(1,4)$. The probability $P(Y\le X)$ is ______ (two decimal places).
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Correct answer: 0.45 to 0.55
Explanation
For fixed X=x in [2,3], P(Y≤x)=(x−1)/3 because Y is uniform on [1,4]. Average over the unit-width X interval: ∫₂³(x−1)/3 dx=[(x−1)²/6]₂³=(4−1)/6=**0.50**.