Question

Let x₁, x₂, ……x_n be values taken by a variable X and y₁, y₂, …….y_n be the values taken by a variable Y such that y_i = ax_i + b, i = 1,2, …….,, n. Then, 

A. Var (Y) = a² Var (X) 

B. Var (X) = a² Var (Y) 

C. Var (X) = Var (X) + b 

D. none of these

Answer 1

we have given, y_i = ax_i + b 

Mean (Y) = \(\frac{\Sigma f_i}{n}\) 

\(\bar Y = \frac{a\Sigma x_n + bn}{n}\) 

Mean (y) = \(\frac{a\Sigma \bar X}{n}+ \frac{nb}{n}\)  

Then, Var(Y) = \(\Sigma \frac{(y_i-\bar Y)^2}{n}\)  

Then, Var (X) = \(\Sigma \frac{(x_i-\bar X)^2}{n}\) 

Hence, Var(Y) = a² Var(X)