Let X ={x ∈ N: 1 ≤ x ≤ 17} and Y ={ a x+ b: x ∈ X and a, b ∈ R, a >0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b…

Let $\displaystyle \mathrm{X}=\{x \in \mathbf{N}: 1 \leq x \leq 17\}$ and $\displaystyle \mathrm{Y}=\{\mathrm{a} x+\mathrm{b}: x \in \mathrm{X}$ and $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{R}, \mathrm{a}>0\}$. If mean and variance of elements of Y are $\displaystyle 17$ and $\displaystyle 216$ respectively then $\displaystyle \mathrm{a}+\mathrm{b}$ is equal to :