Can someone help me with this question.

http://i49.photobucket.com/albums/f2.../Probdense.jpg

Printable View

- May 19th 2009, 10:45 PMFreemymindProbability density function
Can someone help me with this question.

http://i49.photobucket.com/albums/f2.../Probdense.jpg - May 19th 2009, 10:55 PMmr fantastic
a. Where are you stuck with doing the integration?

b. $\displaystyle \mu = E(X) = \int_0^{+ \infty} x a e^{-ax} \, dx$. 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 $\displaystyle m$. Solve $\displaystyle \int_0^{m}a e^{-ax} \, dx = \frac{1}{2}$ for $\displaystyle m$. Show your working and where you get stuck if you can't do this. - May 19th 2009, 11:02 PMmatheagle
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 - May 20th 2009, 09:48 AMFreemymind
For a I got

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

But that does not give me 1 - May 20th 2009, 01:35 PMmatheagle