FRM Part I · FRM Exam Part I · Fundamentals of Probability
A discrete random variable X takes the values -2, 0 and 4 with probabilities 0.25, 0.50 and 0.25 respectively. What is the expected value of X?
The expected value is the probability-weighted sum of outcomes: (-2)(0.25) + 0(0.50) + 4(0.25) = -0.5 + 0 + 1.0 = 0.50. Each outcome is multiplied by its own probability before summing, so the answer is 0.50.
- A0.50Correct
- B1.00
- C0.00
- D2.00
Explanation
E[X] = (-2)(0.25) + 0(0.50) + 4(0.25) = -0.5 + 0 + 1.0 = 0.50. The option 1.00 comes from ignoring the negative sign on -2 (0.5 + 1.0 = 1.5 is not it either), and 0.00 comes from simply averaging the two extreme values with equal weights incorrectly. Only 0.50 follows from the probability-weighted sum.
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