a jury of 12 people is randomly selected from a group of 8 red hat, 7 blue hat,3 green hat and 20 yellow hat potential jurors. Let R, B, G and Y be the # of jurors, respectively. Calculate the joit probability mass function of R,B,G,Y and the marginal probability mass function of R
Since the jurors are chosen (I assume) without replacement, the distribution will actually be the multivariate hypergeometric distribution:
where r + b + g + y = 12.
You could also build in the r + b + g + y = 12 restriction and write the pmf as:
.
The marginal pmf for red will be a hypergeometric distribution:
.
Sorry for the original mistake in interpretation