Answer:
(a) fxy(x,y) = f(x), f(y)
(b) fx(x) = X = (99.3/100) x 4 = 3.972
(c) E(X) = 4
(d) fy/2y = (99.7/100) of (2 x 4) = 7.976
(e) E(Y | X = 2) = 2.
(f) V(Y | X = 2) = 2
Step-by-step explanation:
fxy(x,y) = f(x), f(y), as the question presented the assumption that the devices are independent, their measurements must also be independent
Since the first device is able to accurately detect 99.3% of the defective items it receives and the total defective items sent is 4,
(b) fx(x) = X = (99.3/100) x 4 = 3.972
(c) E(X) is expected result from first device. It is 4 because the items will be whole number.
(d) fy/2y = (99.7/100) of (2 x 4) = 7.976
(Since the first device is able to accurately detect 99.7% of the defective items it receives and the total defective items sent is 4)
(e) E(Y | X = 2) = 2. If the second device measure 2 defective items (X = 2), first device will also detect 2 because the measure 99.3% and 99.7% accurately. Their measurements will be approximately equal.
f. V(Y | X = 2). Like the explanation for (e) above, any relations V(Y | X = 2) will also be 2
(g) X and Y are independent because the are measure
measurements on two different devices
