Topic: Probability and Statistics
Random variable x is with uniform distribution in the span [-4, 1], mean and variance of x is
- A. -1.5, 25/12
- B. -1.5, 5/12
- C. -2.5, 5/12
- D. -2.5, 1/4
Answer: A. -1.5, 25/12
Explanation: For a uniform distribution defined over the interval $[a, b]$, the mean is given by $\mu = \frac{a + b}{2}$ and the variance is $\sigma^2 = \frac{(b - a)^2}{12}$. Here, $a = -4$ and $b = 1$.
Mean $= \frac{-4 + 1}{2} = -1.5$.
Variance $= \frac{(1 - (-4))^2}{12} = \frac{5^2}{12} = \frac{25}{12}$.