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

1. ## 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).

Thanks so much in advance!

2. 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.