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Part CCSIR NET June 2024variance-scales-by-the-square

Variance scales by the square

Let X and Y be independent random variables with X ~ N(2, 4) and Y ~ N(−4, 9) where denotes a normal distribution with mean and variance . Given and where is the cumulative distribution function of a standard normal random variable. Which of the following statements are true?

  1. A.Var(2X + Y) = 17
  2. B.P(|2X + Y| ≤ 15) = 0.9974
  3. C.Cov(3X + 2Y, 3X − 2Y) = 0
  4. D.2X − Y ~ N(0, 25)

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: Uncorrelated ⇒ independent

More on this topic

The chapter behind this: Random variables, moments and generating functions — free to read

From ProbabilityRandom variables, distributions, moments, MGF

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