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Presuming
\(t \lt \frac{1}{\mu}\)
where
\(\mu\)
is the mean waiting time till the first "change" and
\(r\)
is the number of changes desired,
\begin{equation*} M(t) = \frac{1}{ \left ( 1-\mu t \right )^{r}} \end{equation*}
in-context