Let

be a random variable and

be the expected value. Moreover

is defined:

Then the probability measure of

is:

Prove...

It can be noted that there exist both density and cumulative distribution functions over

.

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I have been working on this problem a bit more and found some more info. It seems it is an application of the Markov Property, which states:

Let

be a measurable set with the characteristic function

if

and

otherwise, where

then:

Maybe it is obvious from this but I cannot work out the final details ....

A proof of the markov inequality can be seen on wikipedia..