Explanation:
The variance of a random variable is the probability-weighted average of squared deviations from its expected value. Here, each scenario has an equal probability of 1/3. The expected value (E(X)) is calculated as (2.0 + 2.2 + 2.4)/3 = 2.2. The variance is then computed as [(2.0 - 2.2)² + (2.2 - 2.2)² + (2.4 - 2.2)²]/3 = [0.04 + 0 + 0.04]/3 = 0.08/3 ≈ 0.0267, which rounds to 0.03. Option B represents the standard deviation (the square root of variance), and Option C is the difference between the EPS values, not the variance.
An analyst assumes that a company's future earnings per share (EPS) will be either $2.00, $2.20, or $2.40. Given that each scenario is equally probable, the variance (in $²) of the company's future EPS is most likely:
A
0.03.
B
0.16.
C
0.20.
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