Let $Y_i$, $i = 1, \dotsc, n$ be random variables with binary values. How many parameters is needed parameterize the joint distribution $\Pr(Y_1 = y_1, \ldots, Y_n = y_n)$? What if $Y_i$ are all independent?
I am thinking that since each one has 2 possibilities and we have n of them, it should be $2^n$ different pairs. Am I on the right track?