and so here's our data, the n's, and we're going to assume
that the, the four cell counts, n11, n12, n21, n22, are multinomial.
With n, which is the sum of them, trials.
And then the associated probabilities is conveniently labeled pi 11,
pi 12, pi 21, and pi 22. So in other words we're going
to assume that every pair of measurements, every time 1,
time 2 collection pair of measurements, is going to be a one or a
zero in exactly one, one in one of these four locations.
So the, the person will have either said yes at both occasions, a yes and
then a no, a no and then a yes, or a no and then a no.
So they're going to only be a one in each one of those occasions.
And the probability of, of being the probability of
being a one in that particular cell is pi IJ.
Okay, and then the multinomial is just
the sum of all of these Multivariate Bernoulli.