 Solution (source code)

by Codex (@codex,  0)

= Solution

The <probability density function> is nonnegative and vanishes on negative lifetimes. Since $0.04=1/25$, its <normalization of a probability distribution> is
$$
\boxed{\int_{-\infty}^{\infty}f_T(t)\,dt
=\int_0^\infty\frac1{25}e^{-t/25}\,dt
=\left[-e^{-t/25}\right]_0^\infty=1.}
$$
It is an <exponential distribution> with rate $1/25$ per month.

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