Question 1

Two students are enrolled in a psychology exam. Assume that the probability that student A passes the exam is 80%, and student B 60%. The event that student A passes the exam or not does not affect the performance of student B.

(a)Compute the probability that at least one of the two students will pass the exam.?

(5 marks)

(b)If at least one of the two students passes the exam, what is the probability that student A passes the exam? (5 marks)

Question 2

In an NBA final, two teams A and B play a series of games, capped at 7. The first team who wins a total of four games wins the champion. Assuming the probability that team A wins against team B is 1/3, compute the probability that team A will win the champion. (10 marks)

Question 3

Suppose that ? is a random variable for which ?(?) = ? and ???(?) = ?2. Let ? be an arbitrary constant. Show that ?[?(? ? ?)] = ?(? ? ?) + ?2.

(10 marks)

Question 4

The cumulative probability function (CDF), ?(?), of a random variable ? is sketched below in Figure Q4. Find the corresponding probability.

F(x) A 04 0.2 Figure Q4