Chapter 4.5, Problem 1E

Let X and Y have a bivariate normal distribution with parameters ${\mu }_X=-3,{\mu }_Y=10,{\sigma }_X^2=25,{\sigma }_Y^2=9$ and $\rho =\frac{3}{5}$.

Compute

(a) $P\left(-5<X<5\right)$.

(b) $P\left(-5<X<5|Y=13\right)$.

(c) $P\left(7<Y<16\right)$.

(d) $P\left(7<Y<16|X=2\right)$.