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Suppose I have the following probability density function.

$f(x) = \begin{cases}ce^{-\frac x{200}}&\mathrm{\ if\ } 0

How do I find $c$? Currently, I have the following.

$\int_0^\infty ce^{-\frac x{200}}dx = 1$

$\lim_{x\to\infty} -200ce^{-\frac x{200}} + 200c = 1$

$c = \frac1{200}$

Is this right?

2 Answers 2

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Yes, that is completely correct

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So we want to choose $c$ so that $\int_0^\infty ce^{-x/200}\, dx=1.$

An antiderivative of $ce^{-x/200}$ is $-200ce^{-x/200}$. So our definite integral is $200c$. It follows that $c=1/200$.

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    @idealistikz: Yes, you are right, it wasn't in TeX so I missed it.2012-09-12