Chapter 4.5, Problem 9E

Let X and Y have a bivariate normal distribution. Find two different lines, $a\left(x\right)$ and $b\left(x\right)$, parallel to and equidistant from $E\left(Y|x\right)$, such that $P\left[a\left(x\right)<Y<b\left(x\right)|X=x\right]=0.9544$ for all real x. Plot $a\left(x\right)$, $b\left(x\right)$, and $E\left(Y|x\right)$ when ${\mu }_X=2,$ ${\mu }_Y=-1,$ ${\sigma }_X=3$ ${\sigma }_Y=5,$ and $\rho =\frac{3}{5}$