1) Can I use the variance of the parameter to build confidence intervals like I would with a normal distribution, ie lower 95 CI = mean - 1.96*variance? I recall hearing that the information matrix tends towards normal as n => Inf.

2) If I wanted to know the confidence interval of the product of the two parameters, alpha * beta to get the mean, how could I do that? Can I do the same method as the previous question but just the the Var(A*B) = Var(A) + Var(B) + 2Cov(A,B)? So lower 95 CI = A*B - 1.96*Var(A,B).