A large population of rats had been fed with individually varying mixtures of wholegrain wheat and puffed wheat to see whether the composition of the food has any influence on the lifetimes of the rats. Let \(Y\) be the lifetime of a rat and \(X\) the corresponding ratio of wholegrain it had in its food. An evaluation of (real life) data justifies the assumption that the random vector \((X, Y)\) has a bivariate normal distribution with parameters (in months)

\[\mu_{x}=0.50, \sigma_{x}^{2}=0.028, \mu_{y}=6.0, \sigma_{y}^{2}=3.61, \text { and } ho=0.92\]

With these parameters, \(X\) and \(Y\) are unlikely to assume negative values.

(1) Determine the regression function \(m_{Y}(x), 0 \leq x \leq 1\), and the corresponding residual variance.
(2) Determine the probability \(P(Y \geq 8, X \leq 0.6)\).

You may use software you are familiar with to numerically calculate this probability. Otherwise, only produce the double integral.)