Results 1 to 2 of 2

Thread: please help

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    13

    please help

    umm can someone please just help me start this question

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

    like just help to start or give me any instructions, not solutions.. please?
    like am i supposed to do something like this?:
    $\displaystyle p(\mu|y) $
    Last edited by bubbling; Sep 15th 2009 at 03:07 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2009
    Posts
    13
    hmmm can someone please help??

    ok, so is this what Im meant to do

    $\displaystyle \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 $\displaystyle \sigma^2 $ ?
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum