Fitting distribution to dependent bivariate dataset

[a9192shark]

Hello,

We have a dataset that consists of two variables, X and Y (see attached Excel file) that have some dependence. For a given X we can analyse the distribution of Y and fit a two parameter Weibull distribution reasonably well. Similarly for a given Y we can fit a two parameter Weibull reasonably well. The distributions are fitted by regressing the observed CDF to a two parameter Weibull CDF and maximising the R2 value. The estimation of Alpha and Beta is achieved using Excel Solver.

How can we select and fit a bivariate distribution to provide a joint probability for the data?

The specific question we are trying to answer is :
What is the probability that is X>=2.5 and Y=11.2 where the specified values could be different depending on the data set?

Any help would be appreciated,

Thanks,

Alan.
PS We are also prepared to be told we are doing this completely wrong so do not be shy in telling us!
A.