In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are selected randomly. Let X equal the number who prefer to date nonsmokers and Y equal the number who prefer to date smokers.
(a) Determine the joint pmf of X and Y. Be sure to include the support of the pmf.
(b) Find the marginal pmf of X. Again include the support.