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Very challenging

  1. Sep 25, 2009 #1
    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:

    [tex]Y_i| \mu, \sigma^2[/tex]~[tex]N(\mu,\sigma^2)[/tex]
    use [tex] p(\sigma^2) \propto \frac{1}{\sigma^2} [/tex] and [tex]p(\mu|\sigma^2) = \frac{1}{\sqrt{2\pi}\sqrt{c}\sigma} exp[-\frac{1}{2} \frac {\mu^2}{c \sigma^2}][/tex]

    and show that
    [tex]p(t|y) \propto (1 + \frac{t^2}{n})^{-(\frac{n+1}{2})}[/tex]

    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}) [/tex]

    any guidance would be VERY appreciated because Ive just been staring at this question for the past two days... Thank you?
  2. jcsd
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