Question 1:

Questions posted on Ed Discussion during the exam period follow a Poisson distribution with a rate of 12 questions an hour. a) If the professor watching Ed Discussion takes a ten minute lunch break, what is the probability that at least 1 question arrives during the break? State your answer to three decimal places. b) How long should the professor's break last (in minutes) if they want the probability that no questions are posted during the break to be at least 60%?

Question 2:

Prove or give counterexamples to the following statements: a) If E1 is independent of E2 and E1 is independent of E3, then E1 is independent of 1 E2 E3. b) If E1 is independent of E2, E1 is independent of E3, and E2 E3 = then E1 is independent of E2 E3.

Note: Ei are the events.