9231 P23 - Jun 2017 - Q6 - 5 marks
6157
The independent variables \(X\) and \(Y\) have distributions with the same variance \(\sigma^{2}\). Random samples of \(N\) observations of \(X\) and \(2 N\) observations of \(Y\) are taken, and the results are summarised by
\[\Sigma x=4, \quad \Sigma x^{2}=10, \quad \Sigma y=8, \quad \Sigma y^{2}=102 .\]
These data give a pooled estimate of 10 for \(\sigma^{2}\). Find \(N\).
