Quote by ahuds001
1. The problem statement, all variables and given/known data
Given a bivariate normal distribution with E(x1)=4 and E(x2) = 6 and Var(X) = [3 2.5]
[2.5 7]
Find P(2*x1>x2)
2. Relevant equations
The cdf of this bivariate normal distribution is given by:
f(x1,x2)=1/(2*pi*var(x1)*var(x2)*sqrt(1rho^2)) * e^(0.5*(z/(2*1rho^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 = ((x1E(x1))^2)/var(x1) + ((x2E(x2))^2)/var(x2)  (2*rho*(x1E(x1))*(x2E(x2)))/sqrt(var(x1)*var(x2))
3. The attempt at a solution
The approximate cdf of this bivariate normal distribution is given (in terms of x and y) by:
.041440417*%e^(0.71186*((((x4)^2)/3)+(((y6)^2)/7)(1.09109*(x4)*(y6))/4.582576))
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.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution

Can you figure out the distribution of the single random variable Y = 2*X1  X2?
RGV