1.  You take a multiple choice test for which you are completely unprepared.  You guess each answer with a 0.25 probability of success. 

a. If the test is 50 questions long, what is the probability of getting exactly 3 questions
correct?

b. What is the probability of getting at least one right answer?

c. What is the probability that the first correct answer will be on the 4th question?

d. What is the probability that the fourth correct answer occurs on the 12th question?

2. You flip a fair coin 100 times.  

a. What is the expected value of the number of Heads you get?

b. What is the standard deviation of the number of Heads?

c. If X is the actual number of heads seen, what does Chebychev's probability tell you about the probability that |X - u| >= 20?


3. You roll two fair dice.  Call the resulting numbers R1 and R2.  Let X = R1 + R2 and 
Y = |R1 - R2|.

a.  Show the joint probability mass function P(X, Y). 
b. Calculate the marginal probabilities.
c. Calculate COV(X, Y) and the correlation coefficient.