10. It is known that, with probability 0.6, a new laptop owner will install a wireless Internet connection at home within a month. Let X denote the number (in hundreds)

of new laptop owners in a week from a certain region, and let Y denote the number among them who install a wireless connection at home within a month. Suppose that the PMF of X is

(a) Argue that given X = x, Y ∼ Bin(n = x, p = 0.6), and find the joint PMF of (X,Y).

(b) Find the regression function of Y on X.

(c) Use the Law of Total Expectation to find E(Y).

x 0 1 2 3 4 Px(x) 0.1 0.2 0.3 0.25 0.15