# Probability density function

• May 19th 2009, 11:45 PM
Freemymind
Probability density function
Can someone help me with this question.
http://i49.photobucket.com/albums/f2.../Probdense.jpg
• May 19th 2009, 11:55 PM
mr fantastic
Quote:

Originally Posted by Freemymind
Can someone help me with this question.
http://i49.photobucket.com/albums/f2.../Probdense.jpg

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.
• May 20th 2009, 12:02 AM
matheagle
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).
• May 20th 2009, 10:48 AM
Freemymind
For a I got

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

But that does not give me 1
• May 20th 2009, 02:35 PM
matheagle
Quote:

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 $e^0=1$.