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FRM Part I · FRM Exam Part I · Fundamentals of Probability

A random variable X has E[X] = 3 and E[X^2] = 13. Define Y = 2X + 5. What is Var(Y)?

Var(Y) is 16. First Var(X) = E[X^2] - (E[X])^2 = 13 - 9 = 4. Then for Y = 2X + 5 the constant has no effect and the multiplier is squared, giving 2^2 x 4 = 16.

  1. A16Correct
  2. B8
  3. C13
  4. D21

Explanation

Var(X) = E[X^2] - (E[X])^2 = 13 - 9 = 4. Var(2X + 5) = 4 x Var(X) = 16. The option 8 forgets to square the multiplier (2 x 4), and 21 uses E[Y] = 11 incorrectly mixing in the constant. 13 is just E[X^2].

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