Which of the following statements are correct ?
(A) $var (aX+b)= a^2 var (X)$
(B) $var(X)=E(X^2)-\begin{Bmatrix} E(X)\end{Bmatrix}^2 $
(C) $E(aX+b)=aE(X)+b$
(D) $E(X)=\sum\limits^{n}_{i=1}p_ix^2_i $
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) Only
(A) The variance of a linear transformation $ax+b$ is, $var (aX+b)= a^2 var (X)$
(B) The definition of variance $Var(X)=E(X^2)-\{E(X)\}^2$
(C) The expectation of a linear transformation, $E(aX+b)=aE(X)+b$