4. Suppose (X, Y) has joint p.d.f. fx,x(s, t) = le-sμe-μt (a) Compute the marginal p.d.f. of X (b) Compute the marginal p.d.f. of Y (c) Are X and Y independent? for s, t≥ 0.

Your company determines that the marginal cost, C', of producing the xth unit is given by the function shown below. C'(x) = 4x + 4 Find the total-cost function, C, assuming that C(x) is in dollars and that the total cost of producing 17 units cost $3,851. C(x) =

Your company determines that the marginal cost, C', of producing the xth unit is given by the function shown below. C'(x) = 26x +8 Find the total-cost function, C, assuming that C(x) is in dollars and that the total cost of producing 39 units cost $23,609. C(x) =

The management of Porter Airlines finds that its monthly marginal revenue can be approximated by R'(x) = 0.96 – 0.0064x where x is the average price of a ticket (in dollars) and R'(x) is measured in millions of dollars per dollar. Determine the revenue function R(x). (Hint: If the price of a ticket is zero dollars, the company's revenue is zero dollars.)