Answer: -0.4

## Explanation To generate random variables from U(-1,5) using random variables from U(0,1), we use the inverse transform method. ### Step 1: Find the CDF of X ~ U(-1,5) For a uniform distribution U(a,b), the CDF is: $$F(x) = \frac{x - a}{b - a}, \quad \text{for} \quad a \leq x \leq b$$ Given X ~ U(-1,5), where a = -1 and b = 5: $$F(x) = \frac{x - (-1)}{5 - (-1)} = \frac{x + 1}{6}$$ ### Step 2: Apply the inverse transform method Let U ~ U(0,1), then we solve for X: $$U = F(X) = \frac{X + 1}{6}$$ $$X = 6U - 1$$ ### Step 3: Calculate for U = 0.10 $$X = 6 \times 0.10 - 1 = 0.60 - 1 = -0.40$$ Therefore, the corresponding random variable for U = 0.10 is **-0.40**, which corresponds to option C. ### Verification The transformation X = 6U - 1 maps: - When U = 0 → X = -1 (lower bound) - When U = 1 → X = 5 (upper bound) - When U = 0.10 → X = -0.40 (as calculated)

Author: Tanishq Prabhu