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Trying to figure out this stats problem, but I'm feeling stuck on it:

The PDF for a continuous random variable X is the following:

f(x) = $\{ \frac{c}{x^4} , x>2$ and 0, otherwise

What is the value of c that makes this PDF valid?

It hints that $lim_{n\to \infty} \frac{1}{n^a} = 0$ for any constant a>0.

I'm not quite sure how to interpret this hint or how to solve the problem. Thanks for the help!

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  • $\begingroup$ The hint is probably to draw attention to the fact that a certain improper integral associated with the PDF is convergent (though it does so poorly). What properties does a PDF normally have? One of those is the key to figuring out what the right value of $c$ is. By the way, you should put some part of your question in the title of your post to make it easier for people to notice. $\endgroup$ – CodeLabMaster Feb 23 '17 at 5:04
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To be a PDF, we need that the integral over its domain is equal to 1. So $$\int_2^\infty \frac c{x^4} \, dx =1$$ from which you can integrate and solve for c.

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  • $\begingroup$ Wow, didn't realize it was that simple. Thanks for the help! It makes sense now! $\endgroup$ – SAVen Feb 23 '17 at 4:48

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