Answer: -0.40

## Explanation To generate random variables from U(-1,5) using random variables from U(0,1), we use the inverse transform method. For a uniform distribution U(a,b), the cumulative distribution function (CDF) is: $$F(x) = \frac{x - a}{b - a} \quad \text{for } a \leq x \leq b$$ For X ~ U(-1,5): - a = -1 - b = 5 - b - a = 5 - (-1) = 6 So the CDF is: $$F(x) = \frac{x - (-1)}{6} = \frac{x + 1}{6}$$ To generate X from U ~ U(0,1), we solve for x in terms of u: $$u = \frac{x + 1}{6}$$ $$x + 1 = 6u$$ $$x = 6u - 1$$ Now, for u = 0.10: $$x = 6 \times 0.10 - 1 = 0.60 - 1 = -0.40$$ Therefore, the corresponding random variable from U(-1,5) is **-0.40**. **Verification**: - When u = 0, x = 6×0 - 1 = -1 (lower bound) - When u = 1, x = 6×1 - 1 = 5 (upper bound) - When u = 0.10, x = -0.40 (correct)

Author: Nikitesh Somanthe