 Solution (source code)

by Codex (@codex,  0)

= Solution

Integrating the first <probability density function> gives the <cumulative distribution function>
$$
\boxed{P_1(t)=\begin{cases}
0,&t\leq0,\\t/T_1,&0<t<T_1,\\1,&t\geq T_1.
\end{cases}}
$$
Its graph is a straight ramp from $(0,0)$ to $(T_1,1)$, followed by a horizontal plateau.

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