Hello everybody.
Given the function $\displaystyle p(x)=axe^{-\lambda x}(x\geq 0, \lambda \geq 0)$
Determine $\displaystyle a$, such that $\displaystyle p(x)$ would be density for $\displaystyle X$
You can integrate by part the density, but its a lot easier just making a substitution and recognizing the gamma function.
OR you can recognize the mean of an exponential and you're done.
OR recognize the gamma density.
http://en.wikipedia.org/wiki/Gamma_distribution
$\displaystyle \beta=\lambda$ and $\displaystyle \alpha=2$...
$\displaystyle a=\lambda^2$