Section 3.9.4: "Exponential and Laplace Distributions"

The first line says,"In the context of deep learning, we often want to have a probability distribution with a **sharp point at x=0**." and the author goes on to describe pdf of the exponential distribution in terms of the **indicator function**.

Can anyone help me understand this paragraph in general? What is it meant by "sharp point at x=0", and how does formulating the exponential distribution's pdf in terms of an indicator function help?

Thanks a lot.

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