## Statistics Spring 2013, Quiz Based on Test 1

Name:
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).