 Solution (source code)

by Codex (@codex,  0)

= Solution

For $t_0\geq0$, integration of the <exponential distribution> gives its <cumulative distribution function>:
$$
\boxed{P(0\leq T\leq t_0)=\int_0^{t_0}\alpha e^{-\alpha t}dt=1-e^{-\alpha t_0}.}
$$
For $t_0<0$ the event is empty and its probability is zero.

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