Statistics question bank (Mathematics)

For the probability distribution
Then the $\operatorname{Var}(\mathrm{X})$ is (Given : $\left.(0.25)^2=0.0625,(0.35)^2=0 \cdot 1225,(0.45)^2=0 \cdot 2025\right)$

The raw data $x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$ is an A.P. with common difference $\mathrm{d}$ and first term $0 . \bar{x}$ and $\sigma^2$ are mean and variance of $x_{\mathrm{i}}, \mathrm{i}=1,2, \ldots \ldots \mathrm{n}$, then $\sigma^2$ is