We introduce the Multinomial distribution, which is arguably the most important multivariate discrete distribution, and discuss its story and some of its nice properties, such as being able to "lump" categories together. We also do an example with the Cauchy distribution.
Note: Around 7:39, a factor of the square root of 2 was accidentally
dropped; the result should be 2 over the square root of pi, rather
than the square root of 2 over pi.