If `x_1, x_2, ,\ x_n` are `n` values of a variable `X\ a n d\ y_1, y_2 y_n` are `n` values of variable `Y` such that `y_i=a x_i+b , i=1,2,ddot,\ n` then write `V a r\ (Y)` in terms of `V a r(X)`

Answer

`Var(Y)=a^{2} frac{sum(x_{i}-ar{X})^{2}}{n}=a^{2} Var(X)`

Explanation

`Var(X)=\frac{\sum(x_{i}-\bar{X})^{2}}{n}`



`Var(Y)=\frac{\sum(y_{i}-\bar{Y})^{2}}{n}`



We have: `y_{i}=a x_{i}+b`



`\bar{y}=\frac{\sum y_{i}}{n}=\frac{a \sum x_{i}+n b}{n}=a \bar{X}+b`



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