Introduction to Probability and Statistics Homework 1

Problem 0 Read the first two chapters of your text, A Modern Introduction
to Probability and Statistics: Understanding Why and How.
Problem 1 Two professors and three graduate assistants are responsible
for the supervision of a CS lab, and at least one professor and one graduate
assistant have to be present at all times.
(a) Using two coordinates so that (1,3), for example, represents the event
that one professor and 3 graduate assistant are present, describe the
sample space.
(b) Describe in words the events which are represented by B = f(1; 3); (2; 3)g,
C = f(1; 1); (2; 2)g, and D = f(1; 2); (2; 1)g
(c) With reference to part (b), express C [ D symbolically by listing the
elements and also express it in words.
(d) With reference to part (b) are B and D mutually exclusive?
Problem 2 With reference to the above problem, suppose that each point
(i; j) of the sample space is assigned the probability 15 i+=28 j
(a) Verify that this assignment of probabilities is permissible.
(b) Find the probabilities of the events B, C, and D.
(c) Find the probability that 1, 2, or 3 graduate assistants will be supervising the lab.
Problem 3 The probabilities that a TV station will receive 0; 1; 2; 3; : : : ; 8,
or at least 9 complaints after showing a controversial program are, respectively, 0.01, 0.03, 0.07, 0.15, 0.19, 0.18, 0.14, 0.12, 0.09, and 0.02. What are
the probabilities that after showing such a program the station will receive
(a) at most 4 complaints;
(b) at least 6 complaints;
(c) from 5 to 8 complaints?