when you have that now effectively you can apply this principle to any kind of distribution we saw just a Bernoulli distribution up or down outcome for the thumbtack well how about multinomial where it can take on different values one two three and so forth up to capital K well we received some samples x1 through XM we can just see what's the log likelihood of these samples well is the log of the product of theta 1 to the power how often we have outcome 1 theta to the power half when we have the outcome 2 and so forth and