FRM Part I · FRM Exam Part I · Random Variables
A discrete random variable X takes the values -10, 0, 10 and 30 with probabilities 0.20, 0.30, 0.30 and 0.20 respectively. What is E[X]?
The expected value is 7. It is the probability-weighted sum of the outcomes: -2 plus 0 plus 3 plus 6. Each outcome is multiplied by its own probability and the products are added, rather than taking a simple average of the four values.
- A5
- B7Correct
- C8
- D10
Explanation
E[X] = (-10)(0.20) + 0(0.30) + 10(0.30) + 30(0.20) = -2 + 0 + 3 + 6 = 7. Choosing 5 comes from using a simple average of the middle values, ignoring the probabilities of the tails. Checking: the weights sum to 1.00, so no normalization is needed.
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