You can express a Student-t distribution as a continuous mixture of normal distributions. Some properties of the t distribution are easier to prove in this form. Here are notes with details.
I ran across this tidbit reading Bayesian Data Analysis by Gelman et al.
Related post: Beer, Wine, and Statistics (origin of the Student-t distribution)
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A.M. 10.31.09 at 06:54
I’m doing some research on mixtures, and I was surprised to see that Gelman (in that book, which I will one day find a cheap copy of) does a much better job of explaining the EM algorithm than any of my mixture references.
And it was hands down the best Bayesian book I looked at when trying to do a readings course on the topic last semester.
I think I’m trying to say: Yay Gelman!