1. Probability density function

Can someone help me with this question.

2. Originally Posted by Freemymind
Can someone help me with this question.
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.

3. 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).

4. For a I got

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

But that does not give me 1

5. 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 $\displaystyle e^0=1$.