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Math Help - If X|S ~ N(0,S) and S ~ Inverse-Chisquare(nu), show that X ~ t(nu).

  1. #1
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    Unhappy If X|S ~ N(0,S) and S ~ Inverse-Chisquare(nu), show that X ~ t(nu).

    If X|S ~ N(0,S) and S ~ Inverse-Chisquare(nu), show that X ~ t(nu).

    If X|S ~ N(0,S) and S ~ Inverse-Chisquare(nu), show that X ~ t(nu).-homework.jpg


    Thanks so much in advance!
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm not sure what this inverse chi-square is.
    BUT you should multiple the two densities and then integrate out the S.
    The product of densities of X|S and S with give you the joint of X and S.
    To get the marginal density of X, you then need to integrate out the S variable.
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