I have two distributions which can be fitted by f(x) and by g(y) respectively. To simplify the problem, imagine f(x) is a Gaussian plus a polynomial (representing signal and background respectively) and g(y) is also a Gaussian plus a polynomial. I would like to calculate the probability that x is signal and y is signal. If x and y are independent, I would just calculate the probability for f(x) to be signal and multiply it by the probability of g(y) to be signal. However, if they are not, then how should I proceed? An idea is to plot the pairs (x,y) so that I can use h(z) which would be the PDF that describes the signal and background of the two dimensional distribution. Given that I know f(x) and g(y) is there a way to combine them to form h(z)?
2026-05-04 23:40:12.1777938012
Combining PDF of two variables
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