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CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns

A discrete random variable Y has the following probability distribution: P(Y=1)=0.2, P(Y=2)=0.3, P(Y=3)=0.4, P(Y=4)=0.1. The variance of Y is closest to:

The variance is about 0.84, which is closest to 0.81... see note: the closest listed value is 0.81 only if rounding loosely; the computed value is E(Y²) of 6.6 minus the squared mean 5.76.

  1. A0.81
  2. B0.89Correct
  3. C1.00

Explanation

E(Y) = 0.2 + 0.6 + 1.2 + 0.4 = 2.4. E(Y²) = 0.2(1) + 0.3(4) + 0.4(9) + 0.1(16) = 0.2 + 1.2 + 3.6 + 1.6 = 6.6. Variance = 6.6 - 2.4² = 6.6 - 5.76 = 0.84. Check by deviations: 0.2(1.96)+0.3(0.16)+0.4(0.36)+0.1(2.56)=0.392+0.048+0.144+0.256=0.84.

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