Question

A random variable X is uniformly distributed in the range [0, 5]. The variance and mean square value of X will be respectively equal to

• A. $\frac{25}{12}\text{and}\frac{25}{12}$
• B. $\frac{25}{3}\text{and}\frac{25}{3}$
• C. $\frac{25}{12}\text{and}\frac{25}{3}$
• D. $\frac{25}{3}\text{and}\frac{25}{12}$

Answer 1

The correct option is C $\frac{25}{12}\text{and}\frac{25}{3}$

$\text{Mean,}E\left[X\right]=\frac{0+5}{2}=2.5$

$\text{Variance,}{\sigma }_X^2=\frac{(5-0{)}^2}{12}=\frac{25}{12}$

$\text{Mean square value,}E\left[X^2\right]={\sigma }_X^2+\left(E\right[X]{)}^2$

$=\frac{25}{12}+{\left(\frac{5}{2}\right)}^2=25(\frac{1}{12}+\frac{1}{4})=25\times \frac{4}{12}=\frac{25}{3}$