Standard +0.3 This is a straightforward application of linear transformation properties for normal distributions: E(Y) = a + bE(X) and Var(Y) = b²Var(X). Students need to set up two equations and solve simultaneously, requiring only algebraic manipulation of given parameters. While it involves Further Maths content, the problem is routine and mechanical once the transformation rules are recalled.
8 The Normal variable \(X\) is transformed to the Normal variable \(Y\).
The transformation is \(\mathrm { y } = \mathrm { a } + \mathrm { bx }\), where \(a\) and \(b\) are positive constants.
You are given that \(X \sim N ( 42,6.8 )\) and \(Y \sim N ( 57.2,11.492 )\).
Determine the values of \(a\) and \(b\).
8 The Normal variable $X$ is transformed to the Normal variable $Y$.\\
The transformation is $\mathrm { y } = \mathrm { a } + \mathrm { bx }$, where $a$ and $b$ are positive constants.\\
You are given that $X \sim N ( 42,6.8 )$ and $Y \sim N ( 57.2,11.492 )$.\\
Determine the values of $a$ and $b$.
\hfill \mbox{\textit{OCR MEI Paper 2 2021 Q8 [4]}}