Step 1: Calculate the expected value (mean) of X

E(X) = Σ [x * P(x)] E(X) = (0 * 0.50) + (1 * 0.50) = 0 + 0.50 = 0.50

Step 2: Calculate E(X²)

E(X²) = Σ [x² * P(x)] E(X²) = (0² * 0.50) + (1² * 0.50) = (0 * 0.50) + (1 * 0.50) = 0 + 0.50 = 0.50

Step 3: Calculate variance using the formula Var(X) = E(X²) - [E(X)]²

Var(X) = E(X²) - [E(X)]² Var(X) = 0.50 - (0.50)² Var(X) = 0.50 - 0.25 = 0.25

Step 4: Verify with alternative variance formula

Var(X) = Σ [P(x) * (x - μ)²] Var(X) = 0.50 * (0 - 0.50)² + 0.50 * (1 - 0.50)² Var(X) = 0.50 * (-0.50)² + 0.50 * (0.50)² Var(X) = 0.50 * 0.25 + 0.50 * 0.25 Var(X) = 0.125 + 0.125 = 0.25

Conclusion: The variance of X is 0.25, which corresponds to option A.