when you calculate the Moment of the following equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

p(x)=\left\{\begin{array}{cc}2Axe^{-Ax^2},&\mbox{ if }

x\geq 0\\0, & \mbox{ if } x<0\end{array}\right.

[/tex]

We get

[tex]

Mn =2A \int_0^\infty x^{n+1}e^{-Ax^2}

[/tex]

solving it by parts I am getting

[tex]

Mn=(n+1)\int_0^\infty x^{n-1}e^{-Ax^2}

[/tex]

but, apparently, the right solution is

[tex]

Mn=n\int_0^\infty x^{n-1}e^{-Ax^2}

[/tex]

What am I doing wrong? What is the proper way to solve it? Could you please do it step by step?

Thanks

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# Moment of a probability distribution

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