A tool and die company makes castings for steel stress-monitoring gauges. Their annual profit, Q, in hundreds of thousands of dollars, can be expressed as a function of product demand, y:
Q(y) =2(1−e−2y)
Suppose that the demand (in thousands) for their castings follows an exponential pdf, fY (y) = 6e−6y, y > 0. Find the company’s expected profit.