The prices per unit \(X\) and \(Y\) of two related stocks have a bivariate normal distribution with parameters

\[\mu_{X}=24, \sigma_{X}^{2}=49, \mu_{Y}=36, \sigma_{Y}^{2}=144, \text { and } ho=0.8\]

(1) Determine the probabilities

\[P(|Y-X| \leq 10) \text { and } P(|Y-X|>15)\]

You may make use of software you are familiar with to numerically calculate these probabilities. Otherwise only produce the respective double integrals.
(2) Determine the regression function \(m_{Y}(x)\) and corresponding residual variance.