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Help inequality proof

  1. May 13, 2008 #1
    Can anyone help me prove this inequality?
    See upload~
     

    Attached Files:

  2. jcsd
  3. May 14, 2008 #2
    A complete description
    Prove inequality
    [itex]\begin{equation}
    \int^\infty_0y^\frac{2(n-1)}{n}p(y)\,\mathrm{d}y\Big(\int^\infty_0y^\frac{1}{n}p(y)\,\mathrm{d}y\Big)^2>\int^\infty_0y^\frac{2}{n}p(y)\,\mathrm{d}y\Big(\int^\infty_0y^\frac{(n-1)}{n}p(y)\,\mathrm{d}y\Big)^2
    \nonumber
    \end{equation}[/itex]

    [itex]p(y)>0 [/itex] and [itex]\int^\infty_0p(y)\,\mathrm{d}y=1[/itex] for any y

    n is an integer and [itex]n\ge2$[/itex]
     
  4. May 14, 2008 #3
    When n = 2, both of those inequalities are equal, thus the inequality isn't true for n = 2.
     
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