# If I have N1 samples from PDF p1 and N2 samples from PDF p2, what PDF describes the combined distribution?

If I have (for example) normal distributions $$p_1(x)$$ and $$p_2(x)$$, what PDF (if any) will describe 1000 samples from p1 and 500 samples from p2?

i.e. is there a PDF describing the green histogram $$x_1+x_2$$?

• $x_1+x_2$ is not the ideal way of describing combination of two samples. May 30 '21 at 19:43

If you want to assign priors to distributions, i.e. a RV is $$2/3$$ likely to be drawn from $$p_1$$ and $$1/3$$ likely to be drawn from $$p_2$$, then the new PDF will look like $$p(x)=\frac{2}{3}p_1(x)+\frac{1}{3}p_2(x)$$ And, its histogram will be very much alike the green curve above.