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Math Help - please help

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    13

    please help

    umm can someone please just help me start this question

     Y_i|\mu,\sigma^2 ~ N(\mu,\sigma^2)
    use  p(\sigma^2) \propto \frac{1}{\sigma^2} and  p(\mu|\sigma^2) = \frac{1}{\sqrt{2\pi}\sqrt{c}\sigma} exp[-\frac{1}{2} \frac {\mu^2}{c \sigma^2}] i.e.  \mu|\sigma^2 ~ N (0,c\sigma^2)
    show that
    <br />
p(t|y) \propto (1 + \frac{t^2}{n})^{-(\frac{n+1}{2})}
    where
    <br />
t = \frac{\sqrt{n + 1/c}}{\sqrt{\frac{s}{n} + \frac{\overline{y^2}(1/c)}{(n+1/c)}}} (\mu - \frac{n \overline{y}}{n + 1/c})<br />

    like just help to start or give me any instructions, not solutions.. please?
    like am i supposed to do something like this?:
     p(\mu|y)
    Last edited by bubbling; September 15th 2009 at 04:07 AM.
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  2. #2
    Newbie
    Joined
    Sep 2009
    Posts
    13
    hmmm can someone please help??

    ok, so is this what Im meant to do

     \propto \frac{1}{\sqrt{2\pi}\sqrt{c}\sigma} exp[-\frac{1}{2} \frac {\mu^2}{c \sigma^2}] \times \frac{1}{\sigma^2} \times \prod(\sigma^2)^{-1/2} exp [-1/2 \frac{(Y_i - \mu)^2}{\sigma^2}]

    and then integrate out the  \sigma^2 ?
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