Gain Communications sells aircraft communications units to both the military and the civilain markets. Next year's sales depend on market conditions that cannot be predicted exactly. Gain follows the modern practice of using probability estimates of sales. The military division estimates its sales as follows.
X = units sold 1000 3000 5000 10000
Probability 0.1 0.3 0.4 0.2
The corresponding sales estimates for the civilian division are as follows.
Y = units sold 300 500 750
Probability 0.3 0.5 0.2
We have already calculated the following statistics.
μX = 5000 units; σX2 = 7800000; μY = 490 units; μZ = $11715000, where Z = 2000X + 3500Y
(a) Find the variance and standard deviation of the estimated sales Y of Gain's civilian unit, using the distribution and mean given above.
variance
standard deviation
(b) Because the military budget and the civilian economy are not closely linked, Gain is willing to assume that its military and civilian sales vary independently. Combine your result from (a) with the results above to obtain the standard deviation of the total sales X + Y.
(c) Find the standard deviation of the estimated profit, Z = 2000X + 3500Y.