Let X be the random variable taking values $1,2, \ldots, \mathrm{n}$ for a fixed positive integer n. If $\mathrm{P}(\mathrm{X}=\mathrm{k})=\frac{1}{n}$ for $1 \leq \mathrm{k} \leq \mathrm{n}$, then the variance of X is

• Correct answer
  A

  $\frac{\mathrm{n}^2-1}{12}$
• B

  $\frac{\mathrm{n}^2+1}{12}$
• C

  $\frac{\mathrm{n}^2-1}{6}$
• D

  $\frac{(\mathrm{n}+1)(\mathrm{n}+2)}{6}$

Hence, the correct answer is option: 'A'.