GATE 2025 ST – Question 15

Joint Distributions · Joint and Conditional Distributions · 1 mark · Multiple choice

(X₁,X₂,X₃) is multinomial with 100 trials and probabilities (3/10,1/10,3/5). Find E(X₂|X₃=40).

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Correct answer: (B) 15

Explanation

Conditioning on X₃=40 leaves 60 trials split between categories 1 and 2. The conditional category-2 probability is (1/10)/(1−3/5)=1/4. Thus the conditional mean is 60/4=**15, B**.

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