3) Explain (1) Marginal distribution (2) Conditional Probability & Independence 120] 1. Let X and Y have the joint probability density function given by f

(1) Marginal distribution (2) Conditional Probability & Independence ( [20] 1. Let X and Y have the joint probability density function given by f (x, y ) = 10, 12, 0 0.5). (c) Find the conditional density fox (y|x) with its range. [20] 2. Suppose that X and Y have the following joint probability distribution: p(x,y) 1 3 5 X 2 0.10 0.20 0.10 4 0.15 0.30 0.15 (a) Find the marginal distribution Y. (b) Find E(X-1) and Var(X-1)A telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 100 customers and found that 37% had call waiting. At o =0.01, is there enough evidence to reject the claim