Question: It is not always a trivial task to show that these functions are actually density functions. The condition (5.34) of non-negativity is no problem, but

It is not always a trivial task to show that these functions are actually density functions.

The condition (5.34) of non-negativity is no problem, but some care is required in checking that the functions integrate to 1. For example, to check this for the function given in (5.38) we require the standard definite integral Z

∞

−∞

e−x2 dx = √π.

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