Answer: 0.16

## Explanation The power law describes the probability of observing a random variable X greater than a given value x as: $$P(X > x) = kx^{-\alpha}$$ Where k and α are constants. **Given:** - α = 4 - P(X > 20) = 0.01 **Step 1: Find the constant k** $$0.01 = k \cdot 20^{-4}$$ $$0.01 = k \cdot \frac{1}{20^4}$$ $$0.01 = k \cdot \frac{1}{160,000}$$ $$k = 0.01 \times 160,000 = 1,600$$ **Step 2: Calculate P(X > 10)** $$P(X > 10) = 1,600 \cdot 10^{-4}$$ $$P(X > 10) = 1,600 \cdot \frac{1}{10,000}$$ $$P(X > 10) = \frac{1,600}{10,000} = 0.16$$ Therefore, the probability that X > 10 is 0.16.

Author: Tanishq Prabhu