Solution
= Solution
An integrable nonnegative <probability density> of this form requires $k>0$. Normalization gives $1=A\int_0^\infty e^{-kt}dt=A/k$, so $\boxed{A=k}$. This is the <exponential distribution> with rate $k$.
= Solution
An integrable nonnegative <probability density> of this form requires $k>0$. Normalization gives $1=A\int_0^\infty e^{-kt}dt=A/k$, so $\boxed{A=k}$. This is the <exponential distribution> with rate $k$.