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.
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