3. A virus-infected computer system has 80% probability of not printing correctly, while a virus-free system prints correctly in 95% of the cases. We know that 10% of the computer systems are virus-infected. If a system did not print correctly, what is the probability that it is infected by a virus?
6-7. Two random variables X and Y describe whether the two students study for a quiz: X = 1 is the first student studies and X = 0 if he does not; Y = 1 is the second student studies and Y = 0 if he doesn't. The joint distribution is P(0,0) = 0.1, P(0,1) = 0.3, P(1,0) = 0.4, P(1,1) = 0.2, Find the distribution for X, Y, and for the auxiliary variable U = X * Y (describing when both students study). Are variables X and Y independent? Compute the expected values E(X), E(Y), and E(U), and the variance V(U).