A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume the devices are independent. Determine
(a) fXY (x, y)
(b) fX (x)
(c) E(X)
(d) fY|2 (y)
(e) E(Y) |X = 2)
(f) V(Y|X = 2)
(g) Are X and Y independent?