Easy -1.8 This is a 1-mark multiple choice question testing direct recall of a standard variance formula (Var(aX+b) = a²Var(X)). It requires no calculation or problem-solving, just recognition of a fundamental result that students memorize early in statistics. Significantly easier than average A-level questions.
2 The random variable \(X\) has variance \(\operatorname { Var } ( X )\)
Which of the following expressions is equal to \(\operatorname { Var } ( a X + b )\), where \(a\) and \(b\) are non-zero constants?
Circle your answer. [0pt]
[1 mark]
\(a \operatorname { Var } ( X )\)
\(a \operatorname { Var } ( X ) + b\)
\(a ^ { 2 } \operatorname { Var } ( X )\)
\(a ^ { 2 } \operatorname { Var } ( X ) + b\)
2 The random variable $X$ has variance $\operatorname { Var } ( X )$
Which of the following expressions is equal to $\operatorname { Var } ( a X + b )$, where $a$ and $b$ are non-zero constants?
Circle your answer.\\[0pt]
[1 mark]\\
$a \operatorname { Var } ( X )$\\
$a \operatorname { Var } ( X ) + b$\\
$a ^ { 2 } \operatorname { Var } ( X )$\\
$a ^ { 2 } \operatorname { Var } ( X ) + b$
\hfill \mbox{\textit{AQA Further Paper 3 Statistics 2021 Q2 [1]}}