If X is a random variable and a, b are real numbers, then which of the following statements are true?

(A) $\text{Var(aX+b)} = a^2 \text{Var(X)}$
(B) $\text{E(aX+b)= a E(X) + b}$
(C) $\text{E(ax+b)= a E(X) - E(b)}$
(D) $\text{Var(aX+b)= a Var(X) + b}$

Choose the correct answer from the options given below:

(A) and (B) only

The correct answer is Option (1) → (A) and (B) only **

(A) $\text{Var}(aX+b)=a^{2}\,\text{Var}(X)$ → True

(B) $E(aX+b)=a\,E(X)+b$ → True

(C) $E(aX+b)=a\,E(X)-E(b)$ → False (because $E(b)=b$, so expression becomes $aE(X)+b$, not $aE(X)-b$)

(D) $\text{Var}(aX+b)=a\,\text{Var}(X)+b$ → False (variance does NOT depend on $b$ and uses $a^{2}$, not $a$)

Correct statements: (A) and (B)