Let `x_1, x_2, ...... ,x_n` be values taken by a variable `Xa n dy_1, y_2,.......... ,y_n` be the values taken by a variable `Y` such that`y_i=a x_i+b ,i=1,2, ,ndot` Then,
(a)`V a r(Y)=a^2V a r(X)`
(b) `V a r(X)=a^2V a r(Y)`
(c) `V a r(X)=V a r(X)+b`
(d) none of these

Explanation

`Var(Y)=Var(ax_i + b)`

`=E[y_i-bar y]^2`

`=E[ax_i+b-(a bar x+b)]^2`

`=E[a(x_i- bar x)^2]`

`=a^2.E[(x_i- bar x)^2)]`

`=a^2.Var(X)`

Thus option A is correct.