Hello, I do not understand above pictures's "ODD FUNCTION => 0" part.
I need more detailed explanation on how it becomes to be 0.
Thank you very much.
2026-02-23 00:59:38.1771808378
Probability - can't understand odd function (random variable prob.)
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An odd function is symmetric with respect to the origin.
Mathematically speaking you have $f(x)=-f(-x)$
Consider a function like $f(x)=x^3$,and try to find the integral on $(-1,1)$.
This is an example of odd function where you get the same quantity of negative as positive so the total integral is $0$
The function in your problem is an odd function because $f(z)=-f(-z)$ so the total integral on $(-\infty, \infty ) =0$