SOLUTION MANUAL
All Chapters Included
FOR
CARLTON AND DEVORE’S
PROBABILITY
WITH APPLICATIONS IN ENGINEERING, SCIENCE, AND
TECHNOLOGY
, Table Of Content
Chapter 1 Probability 1
Chapter 2 Discrete Random Variables and Probability 60
Distributions
Chapter 3 Continuous Random Variables 114
and Probability Distributions
Chapter 4 Joint Probability Distributions and 175
Their Applications
Chapter 5 The Basics of Statistical Inference 244
Chapter 6 Markov Chains 284
Chapter 7 Random Processes 322
Chapter 8 Introduction to Signal Processing 372
,Chapter 1
Section 1.1
1.
a. A but not B = A B′
b. at least one of A and B = A B
c. exactly one hired = A and not B, or B and not A = (A B′) (B A′)
2.
a. S = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
b. A = {(1,1), (2,2), (3,3)}
c. B = {(1,1), (1,3), (3,1), (3,3)}
3.
a. S = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213,
4231}
b. Event A contains the outcomes where 1 is first in the list:
A = {1324, 1342, 1423, 1432}.
c. Event B contains the outcomes where 2 is first or second:
B = {2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}.
d. The event A B contains the outcomes in A or B or both:
A B = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}.
A B = , since 1 and 2 can’t both get into the championship game.
A = S – A = {2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213, 4231}.
4.
a. A = {RRR, LLL, SSS}.
b. B = {RLS, RSL, LRS, LSR, SRL, SLR}.
c. C = {RRL, RRS, RLR, RSR, LRR, SRR}.
d. D = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS}
1
, Chapter 1: Probability
e. Event D contains outcomes where either all cars go the same direction or they all go different
directions:
D = {RRR, LLL, SSS, RLS, RSL, LRS, LSR, SRL, SLR}.
Because event D totally encloses event C (see the lists above), the compound event C D
is just event D: C D = D = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL,
SSR, SSL, SRS, SLS, RSS, LSS}.
Using similar reasoning, we see that the compound event C D is
just event C: C D = C = {RRL, RRS, RLR, RSR, LRR, SRR}.
5.
a. A = {SSF, SFS, FSS}.
b. B = {SSS, SSF, SFS, FSS}.
c. For event C to occur, the system must have component 1 working (S in the first position),
then at least one of the other two components must work (at least one S in the second and
third positions): C = {SSS, SSF, SFS}.
d. C = {SFF, FSS, FSF, FFS,
FFF}. A C = {SSS, SSF, SFS,
FSS}. A C = {SSF, SFS}.
B C = {SSS, SSF, SFS, FSS}. Notice that B contains C, so B C
= B. B C = {SSS SSF, SFS}. Since B contains C, B C = C.
6.
a. The 24 = 16 possible outcomes have been numbered here for later reference.
Ho e age mbe
Outcome m Mortg Nu r
1 2 3 4
1 F F F F
2 F F F V
3 F F V F
4 F F V V
5 F V F F
6 F V F V
7 F V V F
8 F V V V
9 V F F F
10 V F F V
11 V F V F
12 V F V V
13 V V F F
14 V V F V
15 V V V F
16 V V V V
b. Outcome numbers 2, 3, 5, 9 above.
2
All Chapters Included
FOR
CARLTON AND DEVORE’S
PROBABILITY
WITH APPLICATIONS IN ENGINEERING, SCIENCE, AND
TECHNOLOGY
, Table Of Content
Chapter 1 Probability 1
Chapter 2 Discrete Random Variables and Probability 60
Distributions
Chapter 3 Continuous Random Variables 114
and Probability Distributions
Chapter 4 Joint Probability Distributions and 175
Their Applications
Chapter 5 The Basics of Statistical Inference 244
Chapter 6 Markov Chains 284
Chapter 7 Random Processes 322
Chapter 8 Introduction to Signal Processing 372
,Chapter 1
Section 1.1
1.
a. A but not B = A B′
b. at least one of A and B = A B
c. exactly one hired = A and not B, or B and not A = (A B′) (B A′)
2.
a. S = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
b. A = {(1,1), (2,2), (3,3)}
c. B = {(1,1), (1,3), (3,1), (3,3)}
3.
a. S = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213,
4231}
b. Event A contains the outcomes where 1 is first in the list:
A = {1324, 1342, 1423, 1432}.
c. Event B contains the outcomes where 2 is first or second:
B = {2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}.
d. The event A B contains the outcomes in A or B or both:
A B = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}.
A B = , since 1 and 2 can’t both get into the championship game.
A = S – A = {2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213, 4231}.
4.
a. A = {RRR, LLL, SSS}.
b. B = {RLS, RSL, LRS, LSR, SRL, SLR}.
c. C = {RRL, RRS, RLR, RSR, LRR, SRR}.
d. D = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS}
1
, Chapter 1: Probability
e. Event D contains outcomes where either all cars go the same direction or they all go different
directions:
D = {RRR, LLL, SSS, RLS, RSL, LRS, LSR, SRL, SLR}.
Because event D totally encloses event C (see the lists above), the compound event C D
is just event D: C D = D = {RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL,
SSR, SSL, SRS, SLS, RSS, LSS}.
Using similar reasoning, we see that the compound event C D is
just event C: C D = C = {RRL, RRS, RLR, RSR, LRR, SRR}.
5.
a. A = {SSF, SFS, FSS}.
b. B = {SSS, SSF, SFS, FSS}.
c. For event C to occur, the system must have component 1 working (S in the first position),
then at least one of the other two components must work (at least one S in the second and
third positions): C = {SSS, SSF, SFS}.
d. C = {SFF, FSS, FSF, FFS,
FFF}. A C = {SSS, SSF, SFS,
FSS}. A C = {SSF, SFS}.
B C = {SSS, SSF, SFS, FSS}. Notice that B contains C, so B C
= B. B C = {SSS SSF, SFS}. Since B contains C, B C = C.
6.
a. The 24 = 16 possible outcomes have been numbered here for later reference.
Ho e age mbe
Outcome m Mortg Nu r
1 2 3 4
1 F F F F
2 F F F V
3 F F V F
4 F F V V
5 F V F F
6 F V F V
7 F V V F
8 F V V V
9 V F F F
10 V F F V
11 V F V F
12 V F V V
13 V V F F
14 V V F V
15 V V V F
16 V V V V
b. Outcome numbers 2, 3, 5, 9 above.
2
