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Two questions:

1)

I saw this definition of expectation value:

E[g(X)] = integral wrt x from -inf to inf of g(x)*f(x)*dx

for some function g(x) of a random variable X and its density function f(x).

Can this be used to derive why convolution gives the density of a random

variable sum?

2)

In cases where the determinant can not be calculated, do convolution give

any hints of the jacobian in the PDF method formula,

Y_PDF(y) = X_PDF(f^-1(y)) / |f'(f^-1(y))| for some Y = f(X) of a random

variable X with known density X_PDF(x)?

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# A Convolution questions

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