Question

Find the marginal distribution of n

Answer 1

\[f(x,n) = ({2x^{n}e^{-3x}})/n! \]
\[x>0; n=0,1,2,...\]

Answer 2

I know that\[f(n) = \int\limits_{0}^{\infty} {(2x^{n}e^{-3x})/n!} dx\]
Can this integral be done without knowing the value of n?