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GATE 2020 ME (ME2) – Question 11

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables and distributions · 1 mark · MTA

The sum of two normally distributed random variables X and Y is ______.

  1. always normally distributed
  2. normally distributed, only if X and Y are independent
  3. normally distributed, only if X and Y have the same standard deviation
  4. normally distributed, only if X and Y have the same mean

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Correct answer: MTA

Explanation

Independent normal variables have a normal sum, but independence is sufficient rather than necessary: correlated jointly normal variables also have normal sums. Marginal normality alone is insufficient. Thus the word “only” makes B incorrect as a universal claim, while A,C,D also fail. The official key awards **marks to all**.