A random variable is uniformly distributed over the interval 2 to 10. Find its variance.

A random variable is uniformly distributed over the interval 2 to 10. Its variance will be 

(A) $\dfrac{16}{3}$ 

(B) 6 

(C) $\dfrac{256}{9}$ 

(D) 36 

Answer: (A) $\dfrac{16}{3}$ 

Explanation: 

The expected value (i.e. the mean) of a uniform random variable $X$ is: 

$E(X) = \dfrac{b + a}{2}$. 

The variance of a uniform random variable $X$ is: 

$Var(X) = \dfrac{(b - a)^2}{12}$. 

Here, $a$ is the minimum value in the distribution, and $b$ is the maximum value. 

For the given problem, $a = 2$ and $b = 12$. 

Therefore, $Var(X) = \dfrac{(10 - 2)^2}{12} = \dfrac{16}{3}$.