Answer: 0.36

## 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.

Author: Tanishq Prabhu