Simple Multinomial Generative model

$1$ poist pesshbu igredets

Consider a very stmple mullinomial model $M$ to generate text in documents.

Let us assume that this mudel $M$ has a fixed vocabufary $$7$ and that we generate a document by sampling one mord at a time from this vocabolery. Furthermore, all the words that are generated by M are independent of each other.

We would like so caphare the fact in our generative model $M$ that some words in $W$ are more likely lo occur in any given document than the othars. So$,$ the first thing that $M$ mpdeis is how akely it is to generate cartain wand winW. We denote this probabilty by $P(w|)={}_4,$ whitie ${}_e$ is a parameter in cor modat M:

Which of the foliowing option$/$s$)$ is$/$are true about the model parmeters $.?$ Choose all that apply from the statements below:

${}_{2}0$

$gra{d}_{0}1$

${\displaystyle \underset{\text{n}\text{e}\text{w}}{\overset{?}{}}}{}_m=1$

Pman $00>1$