The GATE Grind

GATE 2023 MN – Question 16

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

For random variables X and Y, what is E(3X−5Y)?

  1. 3E(X)−5E(Y)
  2. 3E(X)+5E(Y)
  3. 3E(X)−5E(Y)−15E(XY)
  4. E(X)−E(Y)−E(XY)

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Show answer and explanation

Correct answer: (A) 3E(X)−5E(Y)

Explanation

Expectation is linear: a constant multiplier factors out and the expectation of a sum is the sum of expectations. Therefore E(3X−5Y) = 3E(X)−5E(Y), A. No independence assumption or product-moment term is needed.

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