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Yes, this provides good intuition about why it is useful: the PDF of the sum of two random variables is the convolution of the original PDFs. A convolution is a
by jamessb 2y ago
Yes, this provides good intuition about why it is useful: the PDF of the sum of two random variables is the convolution of the original PDFs. A convolution is awkward to work with, but by the convolution theorem it is a multiplication in the Fourier domain. This immediately suggests that the Fourier transform of a PDF would be a useful thing to work with.
If you don't say that this is what you are doing then it all seems quite mysterious.
- creata 2y ago> the PDF of the sum of two random variables is the convolution of the original PDFs (Probably obvious to everyone reading, but the variables should be independent.)
- schmidtleonard 2y agoBut I'd rather assume the variables are independent and then blame statistics when I get the wrong answer!
- bokenator 2y agoThis is a good place to use cumulants. Instead of working with joint characteristic functions, which gets messy, it lets you isolate the effects of correlation into a separate term. The only limitation is that this doesn't work if the moment doesn't exist.