Essay on Markov Chain and Probability

Submitted By ArunMannarsamy
Words: 3728
Pages: 15
Open Document
P1: FXS/ABE

P2: FXS

9780521740524c14.xml

CUAU021-EVANS

July 17, 2008

8:40

C H A P T E R

14

Revision

Revision of
Chapters 10–13
14.1

Multiple-choice questions

Questions marked with a † are based on Chapter 13.
1 Mary and Ann try to guess the month in which the other was born. The probability that both guess correctly is
A

1
2

B

1
6

1
4

C

D

1
24

E

1
144

2 Bag A contains 2 white and 3 black balls. Bag B contains 3 white and 2 black balls. If one ball is drawn from each bag the probability that they are of different colours is
6
10
13
21
24
A
B
C
D
E
25
25
25
25
25
3 Two dice are thrown. The probability of getting a sum that is greater than or equal to 12 is
1
1
1
1
B
C
D
E
A 0
6
12
18
36
4 A group consists of four boys and three girls. If two of them are chosen at random
(without replacement), the probability that a boy and a girl are chosen is
2
4
12
24
27
A
B
C
D
E
7
7
49
49
49
5 If X and Y are mutually exclusive events such that Pr(X) = Pr(Y ), then Pr(X ∪ Y) is
A Pr(X) × Pr(Y)
†

C Pr(Y)

B Pr(X)

E 1

D 0

6 In 1974, England won the toss in 250 of the 500 Tests played. The probability that
England wins the toss exactly 250 times in the next 500 Tests is
A 1
D

500
250

1
2

250

B

1
2

E

500
250

250

C
1
2

1
2

500

500

397
ISBN 978-1-107-67331-1
© Michael Evans et al. 2011
Photocopying is restricted under law and this material must not be transferred to another party.

Cambridge University Press

P1: FXS/ABE

P2: FXS

9780521740524c14.xml

Revision

398

CUAU021-EVANS

July 17, 2008

8:40

Essential Mathematical Methods 1 & 2 CAS

7 If six fair dice are rolled, the probability of getting at least one 4 is
A

4
6

B

5
6

6

C 1−

5
6

6

D

1
6

E

1
3

8 If a card is randomly drawn from a well-shuffled bridge card deck (52 cards), the probability of getting a heart or a jack is
A

1
52

B

5
13

C

4
13

D

7
52

E

1
26

9 A bag contains k red marbles and 1 white marble. Two marbles are drawn without replacement. The probability that both are red is
A

k
(k + 1)2

B

k−1 k+1 C

k k+1 D

2k k+1 E

2 k+1 10 Two cards drawn at random from a pack. i The first card is replaced and the pack shuffled before the second is drawn. ii There is no such replacement.
The ratio of the probabilities that both are aces is
A 8:3

B 5:3

C 4:3

D 17:13

E 52:51

11 The probability of Bill hitting the bullseye with a single shot is 12 . The probability that
Charles does the same is 14 . Bill has 2 shots and Charles has 4. The ratio of the probability of each player hitting the bullseye at least once is
A 64:27

B 2:1

C 32:27

D 192:175

E 64:85

12 The number of arrangements which can be made using all the letters of the word
RAPIDS, if the vowels are together, is
A 30

B 60

C 120

D 240

E 720

13 The number of ways in which n books can be chosen from m + n different books is
(m + n)!
C (m + n)! − n!
B (m + n)! − m!
A
n!
(m + n)!
(m + n)!
D
E m! m!n!
14 The number of different teams of seven which can be selected from a squad of
12 players is
E 396
D 120
C 5040
B 84
A 792
15 The number of four-letter code words which can be made using the letters P, Q, R, S if repetitions are allowed is
A 16

B 24

C 64

D 128

E 256

16 Six cards labelled 1, 2, 3, 4, 5 and 6 are put into a box. Three cards are then drawn from the box (without replacement). The probability that the three cards are all labelled with odd numbers is
1
1
1
1
1
E
D
C
B
A
20
12
8
4
2
ISBN 978-1-107-67331-1
© Michael Evans et al. 2011
Photocopying is restricted under law and this material must not be transferred to another party.

Cambridge University Press

P1: FXS/ABE

P2: FXS

9780521740524c14.xml

CUAU021-EVANS

July 17, 2008

8:40

Chapter 14 — Revision of Chapters 10–13

399

A 6 × 10 + 1 × 9
D 6 + 10 + 9
18 If Pr(A ∩ B) =

B 6 × 10 × 9
E 6 × 10 × 2

C 6 × 10 + 6 × 9

1
1
1 and Pr(B) = and Pr(B|A) = , then
5
2
3
2
1
and Pr(A) =
3
5
3
2
D Pr(A|B) = and Pr(A) =
3
5

1
3
and Pr(A) =
5
5
3
2
C Pr(A|B) = and Pr(A) =
5
5
2
2
E Pr(A|B) = and Pr(A) =
Show More

Related Documents: Essay on Markov Chain and Probability

Consider An Urn That Contains D Amount Of Marbles

Math 416 Wright Fisher Chain Consider an urn that contains d amount of marbles. Some of these marbles are blue and the others are red. Let X0 be the number of blue marbles initially in the urn. At each step in the Markov chain, perform the following procedure: First, double the number of marbles of each color that are in the urn (You will know have a total of 2d marbles in the urn). Second, choose d of these 2d marbles (uniformly, without replacement). Keep the d marbles you choose in…

Words 898 - Pages 4

Computers And Chemical Engineering 26 2002 Essay

procedure for inventory planning with Markov decision process models. Using data collected from a large paper manufacturer, we develop inventory policies for the finished products. To incorporate both variability and regularity of the system into mathematical formulation, we analyze probabilistic distribution of the demand, explore its connection with the corresponding Markov chains, and integrate these into our decision making. In particular, we formulate the Markov decision model by identifying the…

Words 8274 - Pages 34

HMM Study Guide Essay

Hidden Markov Models (HMMs) Joseph A. Giampapa 6 November 2014 garof@cs.cmu.edu www.cs.cmu.edu/~garof Background of HMMs • Best early tutorial: Lawrence R. Rabiner, “A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition,” in Proceedings of the IEEE, Vol. 77, No. 2, February 1989. DOI: 0018-9219/89/020002, URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=18626 • HMMs – Introduced and studied in late 1960s and 1970s – Became popular in the late 1980s • Reasons…

Words 415 - Pages 2

Finite Math Notes Essay

General Video Notes [.1 .7 .6 .4] [.3 .5 .2 .8] [.4 .9 .9 .5] If you are currently in state 2 (i.e. row 2), then the probability you will transition to state 4 in the next observation is .8 (i.e. column 4) Rows are states; columns are probability of being in each state. Reducing Matrices Video Notes 1) When trying to get a 1 in the first row and first column, multiply the row by the reciprocal of the number you want to be zero. ALL OTHER ROWS REMAIN THE SAME. You may also switch…

Words 659 - Pages 3

History Of Apple Inc

have compiled a survey for a number of students at the Queensland Academy of Science, Maths and Technology (QASMT) that helped gather raw data to then mathematically calculate the percentage that prefers Apple Inc. over other brands. Using the Markov Chain procedure, the state of change for every two years (according to the average time it takes for Apple to release a new product) is then calculated and converted into percentage. With 20 students in total surveyed, the results will be compared to…

Words 1920 - Pages 8

Essay On Face Recognition

Face Recognition, as the most successful applications of image analysis and understanding, has recently received significant attention. Recognition implies the tasks of identification or authentication. Identification involves a one-to-many comparison to fetch unknown identity from a set of known possibilities. Authentication involves a one-to-one comparison to verify a claimed identity. Furthermore, closely related to recognition is classification where the problem is to identify a group of individuals…

Words 1994 - Pages 8

pharmacoeconomic Essay examples

PharmacoEconomics (2013) 31:25–48 DOI 10.1007/s40273-012-0008-3 SYSTEMATIC REVIEW A Systematic and Critical Review of the Evolving Methods and Applications of Value of Information in Academia and Practice Lotte Steuten • Gijs van de Wetering • ` Karin Groothuis-Oudshoorn • Valesca Retel Published online: 4 December 2012 Ó Springer International Publishing Switzerland 2012 Abstract Objective This article provides a systematic and critical review of the evolving methods and applications…

Words 14233 - Pages 57

Hidden Markov Models

Hidden Markov Models Sargur N. Srihari srihari@cedar.buffalo.edu Machine Learning Course: http://www.cedar.buffalo.edu/~srihari/CSE574/index.html Machine Learning: CSE 574 0 HMM Topics 1. 2. 3. 4. 5. 6. 7. What is an HMM? State-space Representation HMM Parameters Generative View of HMM Determining HMM Parameters Using EM Forward-Backward or α−β algorithm HMM Implementation Issues: a) b) c) d) e) Length of Sequence Predictive Distribution Sum-Product Algorithm Scaling Factors Viterbi Algorithm…

Words 3628 - Pages 15

Blood Platelet Bank Essay

Solving Blood Platelet Banks Model Using 1 Corresponding Introduction A platelet is a disk-shaped structure found in the blood of all mammals, playing a major role in the coagulation of blood 1; platelets are transfused to patients to treat or prevent bleeding during surgery and other medical conditions associated with platelet deficiency or function defect. Platelets shelf life for transfusion purposes is up to six days; however, due to testing, platelets are generally not released to inventory…

Words 3372 - Pages 14

Call Our Team On 0845 6439 Essay examples

Call our team on 0845 6439 101 AFA M_o_R® Style Exam Answers Correct answers are marked in red. Overviews 1) What is the definition of a risk? a) Anything going wrong in a project b) An uncertain event which should it occur will have an effect on the achievement of objectives c) Anything happening in the future d) Anything bad 2) Where should risk management be carried out? a) In specialist areas such as health and safety or information security, but not in general management because general managers…

Words 1295 - Pages 6