Small question that has been in my head for several days.
$$ E[\exp(iu1_{Z\succeq t})] = \exp(iu)P(Z\succeq t)$$
Is that statement true?
2026-03-25 06:03:56.1774418636
Mean of an exponential of indicator function
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No. $Ee^{iuI_{\{Z\geq t\}}}=e^{iu}P\{Z\geq t\}+P\{Z<t\}$. Note that $e^{iuI_{\{Z\geq t\}}}=1$ on the event $\{Z<t\}$. You have to take this part alos into account.