GATE 2026 ST – Question 30
Probability · Random Variables and Transforms · 1 mark · Numerical answer
Continuous X has CDF F. Let Y=−3ln F(X). Find E(Y) (integer).
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Correct answer: 3 to 3
Explanation
The probability integral transform makes U=F(X) uniform on (0,1). Thus E(Y)=−3∫₀¹ln u du=3. Equivalently −ln U is exponential with mean 1. **3**.
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