Here’s another interesting problem I came across on math.stackexchange: Suppose is a continuous random variable with density and where and are independent and

Show that is a continuous random variable, and that the density of is even, i.e. for each .

Solution: If then

As the distribution function of is differentiable, is continuous, so we may compute the density by differentiation:

By symmetry it is evident that .

Note that this does not depend on the distribution of !

Looks like latex2py is broken. I’ll have to figure out a fix…

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User error, turns out I forgot to switch WordPress to HTML mode -_-

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