Show full solution. To inspect the quality of the screens for mobile phones produced by Company X, two separate inspection devices are used to test the screens for defects. Basically, a specific...

Show full solution.

To inspect the quality of the screens for mobile phones produced by Company X, two separate inspection devices are used to test the screens for defects. Basically, a specific screen is tested once using the two inspection devices. Device 1 can detect the presence of defects 99.3% of the time, whereas Device 2 can detect defects 99.7% of the time. Assume that the 2 devices are operating independently from each other.

One day, four defective screens were sent for inspection.  Let X represent the number of screens that will be correctly tagged as defective by Device 1, while Y represents the number of screens that will be correctly tagged as defective by Device 2. Determine the following:


a.)  f_Y|2

b.)  E(Y|X=2)
c.) V(Y|X=2)
d.) Are X and Y independent? Explain