It is well know that the convolution of two Gaussian probability distribution gives a Gaussian, are there any other choices of initial pdfs that still give a Gaussian after having performed the convultion?
2026-03-30 05:29:18.1774848558
What two probability distributions (other than the Gaussians) convolved together give a Gaussian pdf?
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Given that Fourier transform turns convolution into product, the answer is either trivially no (the only PDF which convolved with itself gives a Gaussian is Gaussian itself) or trivially yes (for any PDF with a nowhere vanishing Fourier transform there is another PDF which convolved with it gives a Gaussian).