EXAMPLE 5.17

It is easily verified that in the insurance scenario of EXAMPLE 5.15, $E\left(X^2\right)=353,500,$ {\sigma }_{X}^{2} = {353},{500} - {\left( {485}\right) }^{2} = {118},{275},$$$${\sigma }_{X} = {343.911}, $E\left(Y^2\right)=2,987,500,$ {\sigma }_{Y}^{2} = 1,721,875,$$$${\sigma }_{Y} = {1312.202} This gives

$$\rho =\frac{136.875}{\left(343,911\right)\left(1312.202\right)}=.303$$