# Eleisha's Segment 8: Some Standard Distributions

To Calculate

1. In Segment 6 (slide 8) we used the improper prior 1/r. Show that this is just a limiting case of a (completely proper) Lognormal prior.

2. Prove that {\rm Gamma}(\alpha,\beta) has a single mode at (\alpha-1)/\beta when \alpha \ge 1.

3. Show that the limiting case of the Student distribution as \nu\rightarrow\infty is the Normal distribution.