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GATE 2026 BM – Question 16

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

X has mean 3 and standard deviation 2. If Y=(X−3)/4, find the standard deviation of Y.

  1. 0.5
  2. 1
  3. 2
  4. 8

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Show answer and explanation

Correct answer: (A) 0.5

Explanation

Subtracting a constant shifts every outcome equally and does not affect variance. Scaling by one fourth scales standard deviation by its absolute value, one fourth. Therefore SD(Y)=2/4=0.5, A; variance would instead scale by one sixteenth.

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