Question

If variance of \(X\) is \(4\), then the variance of \(Y=4X+2\) is

• A. \(64\)
• B. \(16\)
• C. \(4\)
• D. \(0\)

Hint:

For \[ Y=aX+b, \] \[ \boxed{\operatorname{Var}(Y)=a^2\operatorname{Var}(X).} \] Adding a constant does not affect variance.

Answer 1

The Correct Option is A

For a linear transformation, \[ Y=aX+b, \] the variance is given by \[ \operatorname{Var}(Y)=a^2\operatorname{Var}(X). \] Here, \[ a=4,\qquad \operatorname{Var}(X)=4. \] Therefore, \[ \operatorname{Var}(Y) = 4^2\times4 = 16\times4 = 64. \] Hence, \[ \boxed{\operatorname{Var}(Y)=64.} \] Therefore, \[ \boxed{(A)} \] is the correct answer.