OCR MEI Paper 2 2021 November — Question 8

Exam BoardOCR MEI
ModulePaper 2 (Paper 2)
Year2021
SessionNovember
TopicLinear combinations of normal random variables
TypeLinear transformation to achieve target parameters

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 \(b\).