GATE 2023 ST – Question 37

Standard Univariate Distributions · Continuous Distributions · 2 marks · Multiple choice

X has density 1/x² for x≥1,zero otherwise. For Y=ln X,find P(Y<1 | Y<2).

Show answer and explanation

Correct answer: (A) e/(1+e)

Explanation

For y≥0,P(Y≤y)=P(X≤e^y)=1−e^(−y),so Y∼Exp(1). Since {Y<1}⊂{Y<2},the conditional probability is (1−e⁻¹)/(1−e⁻²)=**e/(1+e), A**.

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