Pg. 12: 2.5, 2.8, 2.11, 2.13, 2.16
Pg. 20: 3.19, 3.29, 3.34
Assignment 2.
Pg. 29: 4.5, 4.10, 4.12
Pg. 34: 5.2, 5.4, 5.11, 5.13(b,c,g)
If P(E) = .9 and P(F) = .8, show that P(EF) \ge .7. In general
prove P(EF)\ge P(E) + P(F) -1.
Show that P(exactly one of the events E or F occurs) =
P(E) + P(F) -2P(EF).
Assignment 3.
Pg. 42: 6.2, 6.7, 6.9, 6.13
Pg. 55: 1.9, 1.11, 1.23
A certain town of population size 100,000 has thre newspapers I, II
and III. The proportion of townspeople that read these papers are as
follows:
| I: 10% | I and II: 8% | I and II and III: 1% |
| II: 30% | I and III: 2% | |
| III: 5% | II and III: 4% |
(a) Find the number of people reading only one newspaper.
(b) How many people read at least two newspapers?
(c) How many people do not read any newspapers?
Assignment 4. Due next Tues.
Pg. 57: 1.26, 1.27
Pg. 68: 3.6, 3.10, 3.14
Assignment 5.
Pg. 77: 4.4, 4.6, 4.11, 4.17.
An event F is said to carry negative information bout an event E, and we write
F\downarrow E if P(E|F)\le P(E). Prove or give a counterexample to each of
(a)-(c).
(a) If F\downarrow E, then E\downarrow F,
(b) If F\downarrow E and E\downarrow G, then F\downarrow G,
(c) If F\downarrow E and G\downarrow E, then FG\downarrow E.
Let Q_n denote the probability that in n tosses of a fair coin no run of 3
consecutive heads appears. Show that
Q_n=1/2 Q_{n-1} + 1/4 Q_{n-2} +1/8 Q_{n-3} and Q_0=Q_1=Q_2=1.
Assignment 6.
Pg. 98: 1.1, 1.4, 1.5, 1.8, 1.14.
Pg. 158: 1.2, 1.6, 1.10.
Assignment 7.
Pg. 108: 2.7, 2.11
Pg. 113: 3.3, 3.4
Pg. 159: 1.17, 1.18, 1.20, 1.21
Pg. 166: 2.11, 2.12
Assignment 8.
Pg. 109: 2.18
Pg. 121: 4.4, 4.9, 4.10, 4.13, 4.16
Assignment 9.
Pg. 129: 5.1, 5.3, 5.7, 5.13
Pg. 134: 6.7, 6.8, 6.12
Pg. 139: 7.6, 7.13
Pg. 104: Do exercise 2.1(a).