Let $\;\overline{x}\;,M\;$ and $\;\sigma^{2}\;$ be respectively the mean ,mode and variance of n observations $\;x_{1},x_{2},...,x_{n}\;$ and $\;d_{i}=-x_{i}-a\;,i=1,2,...,n\;$, where a is any number.\[\] Statement I : Variance of $\;d_{1},d_{2},..,d_{n}\;$ is $\;\sigma^{2}\;$\[\] Statement II :Mean and mode of $\;d_{1},d_{2},..,d_{n}\;$ are $\;\overline{x}-a\;$ and $\;-M-a\;$, respectively

Question

(a) Statement I and statement II are both false\[\](b) Statement I and statement II are both true\[\](c) Statement I is true and statement II is false\[\](d) Statement I is false and statement II is true