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IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations

A random variable X takes the values 1, 2, 3 and 4 with probabilities 0.1, 0.2, 0.3 and 0.4 respectively. What is E[X]?

The expectation is 3.0. It is found by weighting each value by its probability: 0.1 + 0.4 + 0.9 + 1.6 = 3.0. The unweighted average of 2.5 is wrong because the probabilities are not equal.

  1. A2.5
  2. B3.0Correct
  3. C3.2
  4. D2.0
  5. 3.5

Explanation

E[X] = 1(0.1) + 2(0.2) + 3(0.3) + 4(0.4) = 0.1 + 0.4 + 0.9 + 1.6 = 3.0. The value 2.5 is the simple average of the values, which ignores the unequal probabilities.

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