GATE 2026 ST – Question 16

Standard Univariate Distributions · Continuous Distributions · 1 mark · Multiple choice

Independent identically distributed normal X,Y satisfy P(X+2Y≤3)=P(2X−Y≥4). Find E(X).

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Correct answer: (B) 7/4

Explanation

Let their mean be μ and variance σ²>0. The two linear combinations have means 3μ,μ and equal variance 5σ². Normal symmetry and strict monotonicity of Φ give (3−3μ)/(√5σ)=(μ−4)/(√5σ). Thus 4μ=7, so **μ=7/4, B**.

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