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 $\displaystyle X$

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- Sep 8th 2009, 02:29 PMjavaxDetermine a...
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 $\displaystyle X$ - Sep 8th 2009, 04:16 PMmatheagle
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 $\displaystyle \alpha=2$...

$\displaystyle a=\lambda^2$