• Sep 13th 2009, 04:03 AM
bubbling
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
$
p(t|y) \propto (1 + \frac{t^2}{n})^{-(\frac{n+1}{2})}$

where
$
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?:
$p(\mu|y)$
• Sep 15th 2009, 03:10 AM
bubbling
$\propto \frac{1}{\sqrt{2\pi}\sqrt{c}\sigma} exp[-\frac{1}{2} \frac {\mu^2}{c \sigma^2}] \times \frac{1}{\sigma^2} \times \prod(\sigma^2)^{-1/2} exp [-1/2 \frac{(Y_i - \mu)^2}{\sigma^2}]$
and then integrate out the $\sigma^2$ ?