Let x̄, M and σ^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…

Let $\displaystyle \bar{x}, \mathrm{M}$ and $\displaystyle \sigma^2$ be respectively the mean, mode and variance of n observations $\displaystyle x_1, x_2, \ldots, x_{\mathrm{n}}$ and $\displaystyle \mathrm{d}_{\mathrm{i}}=-x_{\mathrm{i}}-\mathrm{a}, i=1,2, \ldots, n$, where a is any number.Statement I : Variance of $\displaystyle \mathrm{d}_1, \mathrm{~d}_2, \ldots, \mathrm{~d}_{\mathrm{n}}$ is $\displaystyle \sigma^2$.Statement II : Mean and mode of $\displaystyle \mathrm{d}_1, \mathrm{~d}_2, \ldots, \mathrm{~d}_{\mathrm{n}}$ are $\displaystyle -\bar{x}-\mathrm{a}$ and $\displaystyle -\mathrm{M}-\mathrm{a}$, respectively