Question: Select two products from a batch of 10 containing three defective and seven non-defective products. Let X = 1 or 0 as the first selection from the 10 products is defective or not, and Y = 1 or 0 as the second selection (from the nine remaining products) is defective or not.
(a) Find the marginal distribution of X.
(b) Find the conditional distributions of Y given each of the possible values of X.
(c) Use the results in parts (a) and (b), and the multiplication rule for joint probability mass functions given in (4.3.4), to find the joint distribution of X and Y.
(d) Find the marginal distribution of Y. Is it the same as that of X?
(e) Find the covariance and the linear correlation coefficient of X and Y.