Given a bivariate normal distribution with E(x1)=4 and E(x2) = 6 and Var(X) = [3 2.5]
The cdf of this bivariate normal distribution is given by:
f(x1,x2)=1/(2*pi*var(x1)*var(x2)*sqrt(1-rho^2)) * e^(-0.5*(z/(2*1-rho^2)))
where var(x1) = 3, var(x2) = 7, E(x1)=4 and E(x2) = 6, and rho = 2.5/(sqrt(3)*sqrt(7))
and z = ((x1-E(x1))^2)/var(x1) + ((x2-E(x2))^2)/var(x2) - (2*rho*(x1-E(x1))*(x2-E(x2)))/sqrt(var(x1)*var(x2))
The Attempt at a Solution
The approximate cdf of this bivariate normal distribution is given (in terms of x and y) by:
Taking the integral from (-infinity to 2*x) dy and then from (-infinity to + infinity) dx should do the trick, but I have been unable to do so even using approximations.