Here is a math problem:

Suppose we are told that and are given that . Show that .

Let’s start with the definition of expectation and use integration by parts.

since we are given .

Now using integration by parts, making the natural selection we have:

Recall that and plugging in our selections we get:

Let’s rewrite as . This simplifies to . Let’s plug this back into our equation above:

since plugging in to the first half of our expression just yields . We can’t actually evaluate at infinity, instead we take the limit:

, but recall that we are told and so we are simply left with:

, our desired result.

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