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GATE 2018 ME (ME1) – Question 36

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables and distributions · 2 marks · Multiple choice

Independent normal variables X₁ and X₂ have means 1,1 and standard deviations 1,2 respectively. For Y = X₁ − X₂, which is correct?

  1. Y is normal with mean 0 and variance 1
  2. Y is normal with mean 0 and variance 5
  3. Y has mean 0 and variance 5 but is not normal
  4. Y has mean 0 and variance 1 but is not normal

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Show answer and explanation

Correct answer: (B) Y is normal with mean 0 and variance 5

Explanation

Independent normal variables have a normal difference. Mean is $1-1=0$. Variances add under independence even for subtraction: $1^2+2^2=5$. Answer B.