Acertain college has m freshmen, m sophomores, m juniors, and m seniors. a certain class is a simple random sample of size n students, i. e., all sets of n of the 4m students are equally likely. let x1, . . , x4 be the numbers of freshmen, . . , seniors in the class.

(a) find the joint pmf of x1, x2, x3, x4.

(b) give both an intuitive explanation and a mathematical justification for whether or not the distri- bution from (a) is multinomial.

(c) find cov(x1, x3), fully simplified. hint: 1+x2+x3+x4 =n.

(d) how does cov(x1,x3) compare to if the distribution in (a) were multinomial? why does this make sense?