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i m trying to evaluate the following:

r*x - r*y ≤ g, where r,x,y are nonnegative random variables of different distribution families and g is a constant nonnegative value.

Then, Pr[r*x - r*y ≤ g] = Pr[r*x ≤ g + r*y] = ∫ F

_{r x}(g + r*y)*f

_{r*y}(y) dy, where F(.) and f(.) denote CDF and PDF, respectively.

The above formula works for independent variables. I m not sure if it works for correlated variables (the above are correlated due to the "r" variable in both "r*x" and "r*y").

Any help would be useful.

Thanks