Probability density function

**Freemymind** · May 19th 2009, 10:45 PM

Can someone help me with this question.

**mr fantastic** · May 19th 2009, 10:55 PM

Originally Posted by Freemymind

Can someone help me with this question.

a. Where are you stuck with doing the integration?

b. $\mu = E(X) = \int_0^{+ \infty} x a e^{-ax} \, dx$ . Do this integral using integration by parts. Show your working and where you get stuck if you can't do it.

Let the median be $m$ . Solve $\int_0^{m}a e^{-ax} \, dx = \frac{1}{2}$ for $m$ . Show your working and where you get stuck if you can't do this.

**matheagle** · May 19th 2009, 11:02 PM

In case you're interested this is an exponential random variable, which is a subset of the gamma family.
Also the parameter a needs to be positive, it does have to be in the interval (0,1).
You can check your answer at http://en.wikipedia.org/wiki/Exponential_distribution

**Freemymind** · May 20th 2009, 09:48 AM

For a I got

-e^(-a(b))- (-e^(a(0)) b = infiniti

But that does not give me 1

**matheagle** · May 20th 2009, 01:35 PM

Originally Posted by Freemymind

For a I got

-e^(-a(b))- (-e^(a(0)) b = infiniti

But that does not give me 1

I have no idea what this means and $e^0=1$ .

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