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

Attachment 21417

Thanks so much in advance!

- Apr 10th 2011, 12:42 PMsobadatmathIf 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).

Attachment 21417

Thanks so much in advance! - Apr 10th 2011, 03:16 PMmatheagle
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.