= Solution
\b[The product formula requires independent failure times.] This assumption is not stated in the original PDF. Under that intended assumption, put $s=t/T$ and use the <failure probabilities for two independent lifetimes>:
$$
\boxed{P(t)=P_1(t)P_2(t)=\begin{cases}
0,&t\leq0,\\s^3,&0<t<T,\\1,&t\geq T.
\end{cases}}
$$
Its graph is a cubic increasing from $(0,0)$ to $(T,1)$, convex before reaching its plateau.
Without independence, the marginal distributions do not determine $P(t)$. The <Fréchet inequalities> give the sharp pointwise bounds
$$
\boxed{\max(0,s+s^2-1)\leq P(t)\leq s^2,\qquad0<s<1}.
$$
For example, taking $t_1=TU$ and $t_2=T\sqrt U$ with the same uniform random variable $U$ preserves both prescribed marginals but gives $P(t)=s^2$, rather than $s^3$.
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