Question:
claims size X follows an Lognormal distribution. The two parameters u and s are estimated as (2,100);the covariance matirx of these estimators is (c11: 0.01, c12:-0.1, c21:-0.1, c22:5). Estimate the variance of P(X>500) when calculate using these estimators.

this question is similar to the Exam C ed13 question 27 pg602.but it is P(X>500) instead of mean.
similar question but with Pareto distribution instead of Lognormal dist is example 31H pg 591


i know that my g(u,s) if follow the 1st steps of example 31H
g(u,s)
= 1- P(X<500)
= 1 - integrate( 1/sqrt(2pi) exp(-0.5 u^2) ) du from range of -infinity to (ln x - u)/s
.....

then dont know how to continue

Can anyone show me the complete solution?