Financial Risk Manager Part 1

Calculation of Variance

To calculate the variance of a discrete random variable, we use the formula:

$\text{Var}(Y) = E[Y^2] - (E[Y])^2$

Step 1: Calculate E[Y] (Expected Value)

$E[Y] = \sum y \cdot P(Y = y) = (0 \times 0.3) + (1 \times 0.6) + (2 \times 0.1) = 0 + 0.6 + 0.2 = 0.8$

Step 2: Calculate E[Y²]

$E[Y^2] = \sum y^2 \cdot P(Y = y) = (0^2 \times 0.3) + (1^2 \times 0.6) + (2^2 \times 0.1) = (0 \times 0.3) + (1 \times 0.6) + (4 \times 0.1) = 0 + 0.6 + 0.4 = 1.0$

Step 3: Calculate Variance

$\text{Var}(Y) = E[Y^2] - (E[Y])^2 = 1.0 - (0.8)^2 = 1.0 - 0.64 = 0.36$

Therefore, the variance of Y is 0.36, which corresponds to option B.