gerv13
Sep25-09, 10:36 PM
Hi, can someone please help me just START this question or give me hints on what to do because i have no idea what to do:
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}]
and 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})
any guidance would be VERY appreciated because Ive just been staring at this question for the past two days... Thank you?
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}]
and 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})
any guidance would be VERY appreciated because Ive just been staring at this question for the past two days... Thank you?