- #1
dbb04
- 5
- 0
when you calculate the Moment of the following equation
[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
[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