Subtopic: Mean, median, mode and standard deviation
Question Statement:
For any probability distribution with finite variance $\sigma^2$ and mean $\mu$, the relationship between $\text{Var}(a X + b)$ and $\text{Var}(X)$ is:
Options:
(A) $a^2 \text{Var}(X)$
(B) $a \text{Var}(X) + b$
(C) $a^2 \text{Var}(X) + b^2$
(D) $|a| \text{Var}(X)$
Answer Key:
A
Step-by-Step Solution & Explanation
Scaling shifts variance by $a^2$, while additive constant $b$ does not affect spread: $\text{Var}(a X + b) = a^2 \text{Var}(X)$.