I know that, If $X$ and $Y$ are two independent random variables then $$\phi_{X+Y}(u) =\phi_{X}(u)\cdot\phi_{Y}(u)$$ and
$ \phi_{-X}(u)=\overline{\phi_{X}(u)}$
How to proceed further?any steps to the right direction would be helpful.
2026-03-28 03:00:59.1774666859
for characteristic function $\phi$, prove that $1-|\phi(2u)|^2\le 4( 1-|\phi(u)|^2 )$
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