Harry Wilson, a mechanical engineer at Lehigh manufacturing, has found that the anticipated profitability of a newly developed motion detector for its popu- lar home security device product line can...

Extracted text: Harry Wilson, a mechanical engineer at Lehigh manufacturing, has found that the anticipated profitability of a newly developed motion detector for its popu- lar home security device product line can be estimated as follows: PW = 40.28W (2X - 11) – 77,860 where W is the number of units produced and sold and X is the sales price per unit. Harry also found that W parameter value could occur anywhere over a range of 1,000 to 6,000 units and the X parameter value anywhere between $20 and $40 per unit. Suppose both W and X are statistically independent continuous random variables with the following means and variances: E[W} = 3,500, V[W] = 2,083,333 %3D E[X] 30, V[X] = 33. What is the variance of PW? (a) 2.2309× 10" (c) 2.769 x 10° (b) 4.4618 × 10" (d) 1.118549 x 1013