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Suppose $x$ has density $f(x) = c/x^4$ for $x > 1$ ($(f(x) = 0$ otherwise) where $ c$ is a constant.

Find $c$.

*My steps: $\int_{-\infty}^{\infty} f(x) dx =1$

Simplifies to $c\int_{1}^{\infty} {1}/{x^4} dx=c(-3x^{-3}/-3)|_{0}^{1}$

And I solve $c=1$

Which I know is not correct as the *Solution in the text gives $c = 3$

No idea why this is so difficult for me. I would get this a month ago now it seems I've lost it.

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1 Answer 1

Hint: When you integrated $\dfrac{1}{x^4}$ to get $ \dfrac{-3 x^{-3}}{-3}$, you should not have both multiplied and divided by $-3$.

One is correct, while the other is wrong and should be removed.

Your limits of integration also change for no reason.

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I completely looked at the integral bounds from another question. But yes, I also did make a mistake with the integration. Thanks. –  user115461 Dec 13 '13 at 1:22

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