## Statistics Spring 2013 Test 1

Name:
1. A student uses two email accounts. Spam is sent regularly to
both account: 30% of spam is sent to the UTEP account and 70%
to the gmail account. UTEP filters out 80% of the spam, gmail
filters out 90% of the spam. Overall, what percentage of the
original spam reaches a student?

2. What is the probability that a spyware that tries 100 random
guesses will guess a password consisting of 3 digits and one
lower-case letter?

3. A student who studied for the quiz answers correctly with
probability 90%, while a student who did not study answers
correctly with probability 10%. We know that 80% of the
students studied for the quiz. If a student answered correctly,
what is the probability that he did not study?

4. A computer is connected to three different printers. The
first and the second printers more reliable; for each of them,
the probability of failure is 10%. For the third one, the
probability of failure is 40%. What is the probability that at
least one of the printers is available?

5. In a remote CS Department, among 10 faculty, 5 are good
teachers and 5 are not so good teachers, and a new student does
not know which are good and which are not. What is the
probability that, when a student signs for 3 classes, all his
professors are good?

6-7. Two random variables X and Y describe whether the two
printers are working: X = 1 is the first printer works and X =
0 if it does not; Y = 1 is the second printer works and Y = 0
if it doesn't. The joint distribution is P(0,0) = 0.2, P(0,1) =
0.4, P(1,0) = 0.3, P(1,1) = 0.1, Find the distribution for X,
Y, and for the auxiliary variable U = X + Y - X
* Y (describing when one of the printers work). Are variables X and Y
independent? Compute the expected value E(U) and the variance
V(U).

8. Suppose now that the variables X and Y corresponding to two
printers are independent; the variable X has value 1 with
probability 80% and the variable Y has value 1 with probability
60%. What is then the expected value of the auxiliary variable
U = X + Y - X * Y?

9. A computer virus attacks a folder consisting of 50
executable files. Each files is affected with the probability
0.01. What is the probability that more than 3 files will be
affected by the virus?