Solutions Manual: Statistics for Business & Economics [1, 8th ed.] 0324066759, 9780324066753

Citation preview

Solutions Manual to Accompany

Statistics for Business and Economics Eighth Edition

David R. Anderson University of Cincinnati

Dennis J. Sweeney University of Cincinnati

Thomas A. Williams

Rochester Institute of Technology

 2002 by South-Western/Thomson Learning Cincinnati, Ohio

Contents Chapter

1. Data and Statistics

2. Descriptive Statistics: Tabular and Graphical Approaches 3. Descriptive Statistics: Numerical Methods 4. Introduction to Probability

5. Discrete Probability Distributions

6. Continuous Probability Distributions

7. Sampling and Sampling Distributions 8. Interval Estimation

9. Hypothesis Testing

10. Statistical Inference about Means and Proportions With Two Populations 11. Inferences about Population Variances

12. Tests of Goodness of Fit and Independence

13. Analysis of Variance and Experimental Design 14. Simple Linear Regression 15. Multiple Regression

16. Regression Analysis: Model Building 17. Index Numbers 18. Forecasting

19. Nonparametric Methods

20. Statistical Methods for Quality Control 21. Sample Survey

Preface The purpose of Statistics for Business and Economics is to provide students, primarily in

the fields of business administration and economics, with a sound conceptual introduction

to the field of statistics and its many applications. The text is applications-oriented and has been written with the needs of the nonmathematician in mind.

The solutions manual furnishes assistance by identifying learning objectives and providing detailed solutions for all exercises in the text.

Acknowledgements

We would like to provide special recognition to Catherine J. Williams for her efforts in preparing the solutions manual. David R. Anderson Dennis J. Sweeney

Thomas A. Williams

1 Data and Statistics 

Learning Objectives

                  u  



          v    v   y  u   t



   u     tw qualitative, quantitative, crossectional and time series data.

4.

Learn about the sources of data for statistical analysis both internal and external to the firm.

5.

Be aware of how errors can arise in data.

6.

Know the meaning of descriptive statistics and statistical inference.

7.

Be able to distinguish between a population and a sample.

8.

Understand the role a sample plays in making statistical inferences about the population.




Chapter 1

!"#$%!&':

1. 2.

3.

4.

5.

Statistics can be referred to as numerical facts. In a broader sense, statistics is the field of study dealing with the collection, analysis, presentation and interpretation of data. a.

9

b.

4

c.

Country and room rate are qualitative variables; number of rooms and the overall score are quantitative variables.

d.

Country is nominal; room rate is ordinal; number of rooms and overall score are ratio.

a.

Average number of rooms = 808/9 = 89.78 or approximately 90 rooms

b.

2 of 9 are located in England; approximately 22%

c.

4 of 9 have a room rate of $$; approximately 44%

a.

10

b.

Fortune 500 largest U.S. industrial corporations

c.

Average revenue = $142,275.9/10 = $14,227.59 million

d.

Using the sample average, statistical inference would let us estimate the average revenue for the population of 500 corporations as $14,227.59 million.

a.

3

b.

Industry code is qualitative; revenues and profit are quantitative.

c.

Average profit = 10,652.1/10 = $1065.21 million

d.

8 of 10 had a profit over $100 million; 80%

e.

1 of 10 had an industry code of 3; 10%

6.

Questions a, c, and d are quantitative. Questions b and e are qualitative.

7.

8.

a.

The data are numeric and the variable is qualitative.

b.

Nominal

a.

2,013

b.

Qualitative

c.

Percentages since we have qualitative data

1-2

Data and Statistics

9.

d.

(0.28)(2013) = 563.64 Must have been 563 or 564.

a.

Qualitative

b.

30 of 71; 42.3%

10. a.

Quantitative; ratio

b.

Qualitative; nominal

c.

Qualitative (Note: Rank is a numeric label that identifies the position of a student in the class. Rank does not indicate how much or how many and is not quantitative.); ordinal

d.

Qualitative; nominal

e.

Quantitative; ratio

11. a.

Quantitative; ratio

b.

Qualitative; ordinal

c.

Qualitative; ordinal (assuming employees can be ranked by classification)

d.

Quantitative; ratio

e.

Qualitative; nominal

12. a.

The population is all visitors coming to the state of Hawaii.

b.

Since airline flights carry the vast majority of visitors to the state, the use of questionnaires for passengers during incoming flights is a good way to reach this population. The questionnaire actually appears on the back of a mandatory plants and animals declaration form that passengers must complete during the incoming flight. A large percentage of passengers complete the visitor information questionnaire.

c.

Questions 1 and 4 provide quantitative data indicating the number of visits and the number of days in Hawaii. Questions 2 and 3 provide qualitative data indicating the categories of reason for the trip and where the visitor plans to stay.

13. a.

Quantitative

b.

Time series with 7 observations

c.

Number of riverboat casinos.

d.

Time series shows a rapid increase; an increase would be expected in 1998, but it appears that the rate of increase is slowing.

14. a.

4

b.

All four variables are quantitative.

c.

Time series data for 1993 to 1996.

1-3

Chapter 1 15.

Crossectional data. It is based on the 1996 performance data that was available April 1997.

16. a.

We would like to see data from product taste tests and test marketing the product.

b.

Such data would be obtained from specially designed statistical studies.

17.

Internal data on salaries of other employees can be obtained from the personnel department. External data might be obtained from the Department of Labor or industry associations.

18. a.

(48/120)100% = 40% in the sample died from some form of heart disease. This can be used as an estimate of the percentage of all males 60 or older who die of heart disease.

b. 19. a.

The data on cause of death is qualitative. All subscribers of Business Week at the time the 1996 survey was conducted.

b.

Quantitative

c.

Qualitative (yes or no)

d.

Crossectional - 1996 was the time of the survey.

e.

Using the sample results, we could infer or estimate 59% of the population of subscribers have an annual income of $75,000 or more and 50% of the population of subscribers have an American Express credit card.

20. a.

56% of market belonged to A.C. Nielsen $387,325 is the average amount spent per category

b.

3.73

c.

$387,325

21. a.

The two populations are the population of women whose mothers took the drug DES during pregnancy and the population of women whose mothers did not take the drug DES during pregnancy.

b.

It was a survey.

c.

63 / 3.980 = 15.8 women out of each 1000 developed tissue abnormalities.

d.

The article reported twice as many abnormalities in the women whose mothers had taken DES during pregnancy. Thus, a rough estimate would be 15.8/2 = 7.9 abnormalities per 1000 women whose mothers had not taken DES during pregnancy.

e.

In many situations, disease occurrences are rare and affect only a small portion of the population. Large samples are needed to collect data on a reasonable number of cases where the disease exists.

22. a.

All adult viewers reached by the Denver, Colorado television station.

b.

The viewers contacted in the telephone survey.

c.

A sample. It would clearly be too costly and time consuming to try to contact all viewers.

1-4

Data and Statistics 23. a.

Percent of television sets that were tuned to a particular television show and/or total viewing audience.

b.

All television sets in the United States which are available for the viewing audience. Note this would not include television sets in store displays.

c.

A portion of these television sets. Generally, individual households would be contacted to determine which programs were being viewed.

d.

The cancellation of programs, the scheduling of programs, and advertising cost rates.

24. a.

This is a statistically correct descriptive statistic for the sample.

b.

An incorrect generalization since the data was not collected for the entire population.

c.

An acceptable statistical inference based on the use of the word estimate.

d.

While this statement is true for the sample, it is not a justifiable conclusion for the entire population.

e.

This statement is not statistically supportable. While it is true for the particular sample observed, it is entirely possible and even very likely that at least some students will be outside the 65 to 90 range of grades.

1-5

+,-./01 2

D03415./560 7/-/53t543: 8-9:;-1 -1-.,54-; ?0t ABCDEFEG HIJBKFtLBM *N

OPQRS TUV WU XUSYWRZXW QS[ \SWPR]RPW YZ^^QR\_QW\US ]RUXP[ZRPY `UR aZQb\WQW\cP [QWQ YZXT QY d `RPaZPSXyQS[ RPbQW\cP `RPaZPSXy[\YWR\eZW\USYf eQR gRQ]TY QS[ ]\P XTQRW YN

(N

OPQRS TUV WU XUSYWRZXW QS[ \SWPR]RPW WQeZbQR YZ^^QR\_QW\US ]RUXP[ZRPY `UR aZQSW\WQW\cP [QWQ YZXT QYd `RPaZPSXyQS[ RPbQW\cP `RPaZPSXy[\YWR\eZW\USYf XZ^ZbQW\cP `RPaZPSXyQS[ XZ^ZbQW\cP RPbQW\cP `RPaZPSXy[\YWR\eZW\USYN

hN

OPQRS TUV WU XUSYWRZXW Q [UW ]bUWf Q T\YWUgRQ^f QS[ QS Ug\cP QY gRQ]T\XQb YZ^^QR\PY U` aZQSW\WQW\cP [QWQN

iN

jP QebP WU ZYP QS[ \SWPR]RPW WTP P]xbURQWURy[QWQ QSQbkY\Y WPXTS\aZP U` Q YWP^

lN

OPQRS TUV WU XUSYWRZXW QS[ \SWPR]RPW XRUYY WQeZbQW\USY QS[ YXQWWPR [\QgRQ^Y U` e\cQR\QWP [QWQN

()*

)QS[)bPQ` [\Y]bQNy

mnopqrs t vwxyz{w|}: ~

Class A B C

t o ‡

Relative Frequency 60/120 = 0.50 24/120 = 0.20 36/120 = 0.30 1.00

~ u €tt  ~‚  ƒ„… † t„ t„€t„„… † ƒ„

ˆ‰Š

”

Frequency 60 24 36 120

m‹oŒŒ ’ “ m – —˜qo‹

o

”•„°™‚‰~t„ x † ~šƒ°

‡

”•„°ƒt‰~t„ x † ~t•°

srŽrˆy tt€t„„… † ƒƒ ~‚€t„„… † ”• ƒ„€t„„… † ‚„ t„€t„„… † ƒ„ t„„

‘rsˆrq srŽrˆy tt ~‚ ƒ„ t„ ~„„

ˆ £¤ ¥¦§¨§¤¨ ©ª «¢ ›œ žŸ ¡¢ £¤ ¡¬¢

tut

­®¯°±²³´²µ® ¶´·´²¯´²°¯¸ ¹·º»¼·± ·½¾ ¿±·³À²°·¼ Á®´À¾¯

¾Æ

70 60 Frequency

50 40 30 20 10 0 Yes

No

No Opinion

Response ÇÆ

·Æ

¹À® ¾·´· ·±® È»·¼²´·´²µ®Æ

ºÆ ¹É ¶ÀÂÊ Á²¼¼²Â½·²±® ˱·¯²®± ÑÀ²°·Ò Ó³® ÑÀ·±Õ®¾ ¹Â´·¼¸

˱®È»®½°y ÃÇ ÎÏ Ô Ç ÏÐ

ÃÄÅ

Ì®±°®½´ ˱®È»®½°y ÇÍ ÅÐ ÎÇ Í ÎÐÐ

Ö×ØÙÚÛÜ Ý

àá

30

Frequency

25 20 15 10 5 0 Millionaire

Frasier

Chicago

Charmed

TV Show

Charmed 8% Chicago 14% Millionaire 48%

Frasier 30%

âá íá

Øá

ãäååäæçØäÜÛ ×Øè Ú×Û åØÜéÛèÚ êØÜëÛÚ è×ØÜÛá ìÜØèäÛÜ äè èÛàæçâá ãØîæÜ ãØçØéÛêÛçÚ ùààæòçÚäçé ìäçØçàÛ ãØÜëÛÚäçé üæÚØå

ïÛåØÚäðÛ ìÜÛñòÛçày ííôÝõö ÷ øáÝí íõôÝõö ÷ øáÝß ÝúôÝõö ÷ øáõû úÝôÝõö ÷ øáûú õáøø

ÝÞß

óÛÜàÛçÚ ìÜÛñòÛçày Ýí Ýß õû ûú õøø

ýþÿ
þ ÿ ÿ   
  
  þÿ



90 80

Frequency

70 60 50 40 30 20 10 0 Management

Accounting

Finance

Major 

þ 




#$$%&"

()*

(+*

 !"

'"$ ,-*

-.*

/

 01 4 5 ÿ   
þ  þy ý :; þ

2
þ3þ y 67 6/ 8 69 /



þ
þ  2
þ3þ y 6/// //4 677 6/4 6777

Marketing

?@AB C

F@=AB JK@>LM

E EH

GHIHH GHHIHH

The Ernst & Young Tax Guide 2000 NO@= > PBAQRASTyKP UV Investing for Dummies NO@= > PBAQRASTy KP CV >SW What Color is Your Parachute? 2000 NO@= > PBAQRASTyKP G >BA XBKR?AW OS @=A YF@=ABY T>@AXKBIy ZI

J=A B>S[ KBWAB PBK\ POB]@ @K POP@= O]M ^OLLOKS>OBAV _>WV ` a>ZO@]V ^K@LAVy>SW bcd eROWAI

TI

J=A ?ABTAS@ KP ]>LA] BA?BA]AS@AW Zy The Millionaire Next Door >SW Rich Dad, Poor Dad O] fgIUUhI

`I

Rating Outstanding Very Good Good Average Poor

Frequency 19 13 10 6 2 50

Relative Frequency 0.38 0.26 0.20 0.12 0.04 1.00

^>S>XA\AS@ ]=KRLW ZA ?LA>]AW NO@= @=A]A BA]RL@]I Efh KP @=A B>@OSX] >BA iAByXKKW @K KR@]@>SWOSXI gfh KP @=A B>@OSX] >BA XKKW KB ZA@@ABI BOSX @=A]A B>@OSX] NO@= ?BAiOKR] BA]RL@] NOLL ]=KN N=A@=AB KB SK@ @=A BA]@>RB>S@ O] \>[OSX O\?BKiA\AS@] OS O@] B>@OSX] KP PKKW QR>LO@jI gI

>I

Position Pitcher Catcher 1st Base 2nd Base 3rd Base Shortstop Left Field Center Field Right Field

sI

Frequency 17 4 5 4 2 5 6 5 7 55

ZI

kO@T=AB] lmL\K]@ UGhn

TI

UBW o>]A lU D fhn

WI

pOX=@ qOALW lmL\K]@ GUhn

AI

rSPOALWAB] lGE KB CsIGhn @K FR@POALWAB] lGg KB UCI`hn

Relative Frequency 0.309 0.073 0.091 0.073 0.036 0.091 0.109 0.091 0.127 1.000

>tZI

Starting Time 7:00 7:30 8:00 8:30 9:00

Frequency 3 4 4 7 2 20

CDE

Percent Frequency 15 20 20 35 10 100

uvwxyz{|z}v ~||zw|zxw€ ‚ƒ„y …† ‡y{ˆzx„ ‰v|ˆŠ†w

xŽ

y ‡y{ˆ

8 7

Frequency

6 5 4 3 2 1 0 7:00

7:30

8:00

8:30

9:00

Starting Time †Ž ‘’’ “’”

˜‘’’ “—” ˜‘–’ ™’”

•‘–’ –—” •‘’’ ™’”

vŽ  ŸŽ Ž

ˆv šŠw| {yv›vyyv† w|y|z…œ |zšv zw €žŸ ŽšŽŽ ~|y|z…œ |zšvw Š› €žŸ …† €ŸŸ ŽšŽ yv …v|xŽ ˆv †| yv›vy |Š ¡ƒ„z|¢ „v}v„w Š› {ŠŠy£ ›zy£ œŠŠ†£ }vyyœŠŠ† …† vxxv„„v…|Ž

‚Ž

Rating Poor Fair Good Very Good Excellent

Frequency 2 4 12 24 18 60

‹Œ

Relative Frequency 0.03 0.07 0.20 0.40 0.30 1.00

¤¥¦§¨©ª «

®¯

°¦ª ±ª¦§¥

30

Frequency

25 20 15 10 5 0 Poor

Fair

Good

Very Good

Excellent

Rating ²³© ¤¥¦ª¨

´µ¶· ¸¹¹· ÉÇ

ÈÇ

Á¹¹Â ÅÆÇ

º»¼½¾¾½¿À ÉÆÇ

˯

ý·Ä Á¹¹Â ÊÆÇ

Ì¥© ®ÍΪϩ ©Ð¦ÑΦ¨³ÍÒ Ë¦¨¦ ³Ò˳®¦¨© ¦ ¥³Ó¥ ÔΦѳ¨Õ ®ÍΪϩ¯ Ì¥© ÖÍϨ ®ÍÖÖÍÒ ª¦¨³ÒÓ ³Ï ЩªyÓÍÍË ×³¨¥ ¨¥© Ï©®ÍÒË ÖÍϨ ®ÍÖÖÍÒ Ø©³ÒÓ ©®x©ÑÑ©Ò¨¯

ÙÙ¯ ¤Ñ¦ÏÏ

Úª©ÔΩҮy

۩Ѧ¨³Ð© Úª©ÔΩҮy

²©ª®©Ò¨ Úª©ÔΩҮy

Ù«¬ÙÜ ÙÞ¬Ùß Ù­¬«Ý «Ù¬«à «Ü¬«á

« ­ ÙÙ ÙÝ â

ݯÝÞÝ Ý¯«ÝÝ Ý¯«ßÞ Ý¯«ÞÝ Ý¯««Þ

Þ¯Ý «Ý¯Ý «ß¯Þ «Þ¯Þ ««¯Þ

«¬­

ãäåæçèéêèëä ìêíêèåêèæåî ïíðñòíç íóô õçíéöèæíò ÷äêöøôå

ïøêíò

üý

þÿýýý

þýýÿý

þùÿ

Class less than or equal to 19 less than or equal to 29 less than or equal to 39 less than or equal to 49 less than or equal to 59

Cumulative Frequency 10 24 41 48 50

Cumulative Relative Frequency .20 .48 .82 .96 1.00

þ ÿ

18 16

Frequency

14 12 10 8 6 4 2 0 10-19

20-29

30-39

40-49

50-59
















ùúû







  

 















Class 6.0 - 7.9 8.0 - 9.9 10.0 - 11.9 12.0 - 13.9 14.0 - 15.9

Frequency 4 2 8 3 3 20

Percent Frequency 20 10 40 15 15 100

 

Waiting Time 0-4 5-9 10 - 14 15 - 19 20 - 24 Totals

Frequency 4 8 5 2 1 20

Relative Frequency 0.20 0.40 0.25 0.10 0.05 1.00



Waiting Time Less than or equal to 4 Less than or equal to 9 Less than or equal to 14 Less than or equal to 19 Less than or equal to 24 

Cumulative Frequency 4 12 17 19 20

Cumulative Relative Frequency 0.20 0.60 0.85 0.95 1.00

  

   !" #$%   --  --.  .--  --  --  --0 +

*+ ", &'()y    /  / 

&'()y       

  

!) &'()y    /  / 

12345678692 :8;8638643< =;>?@;5 ;AB C5;7D64;@ E28DFB3

12

Frequency

10 8 6 4 2 0 10.0019.99

20.0029.99

30.0039.99

40.0049.99

50.0059.99

60.0069.99

Stock Price E;AyFJ 8D232 ;52 @FK 75642B 38F4L3 K68D 8D2 M52;8238 J52N?2A4y6A 8D2 OIPQPP 8F OIRQRR 5;AM2Q >Q

S;5A6AM3 725 :D;52 TOU HYQPP 8F HGQPI HGQPP 8F HIQPI HIQPP 8F HPQPI PQPP 8F PQRR IQPP 8F IQRR GQPP 8F GQRR =F8;@

W2@;8692 V52N?2A4y PQPZ PQPP PQPZ PQY[ PQY[ PQIG IQPP

V52N?2A4y G P G R R Y G\

G H II

X2542A8 V52N?2A4y Z P Z Y[ Y[ IG IPP

]^_`abc d

Frequency

10 9 8 7 6 5 4 3 2 1 0 -3.00 to -2.01

-2.00 to -1.01

-1.00 to -0.01

0.00 to 0.99

1.00 to 1.99

2.00 to 2.99

Earnings per Share g^b h_ijckal jm njh`_okbp ^_q b_cokorp ko a^b stutt aj sdutt c_orbu vjwc jm a^b njh`_okbp xjpa hjobuy fyu

Call Duration 2 - 3.9 4 - 5.9 6 - 7.9 8 - 9.9 10 - 11.9 Totals

Frequency 5 9 4 0 2 20

Relative Frequency 0.25 0.45 0.20 0.00 0.10 1.00

Frequency

zkpajrc_h

10 9 8 7 6 5 4 3 2 1 0 2.0 - 3.9

4.0 - 5.9

6.0 - 7.9 Call Duration

d e fd

8.0 - 9.9

10.0 - 11.9

{|}~€‚€ƒ| „‚…‚€}‚€~}† ‡…ˆ‰Š… …‹Œ …Ž€~…Š |‚ŽŒ} —˜|}‚ }…Š…†y™š”›œœœ €žŽ|}‚ }…Š…†y™“Ÿ•›œœœ

“•– …– ˆ–

„…Š…y  ™“œœœ}¡ š“’“œ¦ “œ¨’“‘œ “‘“’“”¦ “”¨’“¦œ “¦“’“¨¦ “¨¨’“•œ ‡‚…Š

¤|Š…‚€ƒ| ¢|£‰|‹~y œ–œ• œ–“œ œ–‘‘ œ–”¨ œ–“• œ–œ¨ “–œœ

¢|£‰|‹~y § ¦ ““ “• š ” ¦œ

~–

¥‚€‹ ™“”¦›œœœ  Š|}}† ‘œ©¦œ–

Œ–

¥|~|‹‚…ž| more than ™“¦œ›œœœ† ‘§ª

¥|~|‹‚ ¢|£‰|‹~y • “œ ‘‘ ”¨ “• ¨ “œœ

20 18 16

Frequency

14 12 10 8 6 4 2 0 91-105

106-120 121-135 136-150 151-165 166-180 Salary ($1000s)

|– “š– …©ˆ–

Number 140 - 149 150 - 159 160 - 169 170 - 179 180 - 189 190 - 199 Totals

Frequency 2 7 3 6 1 1 20

‘ ’ “”

Relative Frequency 0.10 0.35 0.15 0.30 0.05 0.05 1.00

«¬­®¯°± ²

¶·¸¹

Number Less than or equal to 149 Less than or equal to 159 Less than or equal to 169 Less than or equal to 179 Less than or equal to 189 Less than or equal to 199

Cumulative Frequency 2 9 12 18 19 20

Cumulative Relative Frequency 0.10 0.45 0.60 0.90 0.95 1.00

°¹ ½¼ ÈÇ »º Æà ŠÄÃ

 »¼ Á º

»¾¼ ²É¹ ­¹

»¿¼

»À¼

½¼¼

ʬ° ®°±¶°Ë¯­Ì° ÍÎ ®°Í®Ï° е ͱ Ï°ÑÑ ÒÑ ²É¹É Ó Ô¹Õ Ó Ö¹× Ó ´Ð¹× Ø µÙ¹Ö¹

Ú¹

ʬ° ®°±¶°Ë¯­Ì° ÍÎ ¯¬° ®Í®ÛÏ­¯ÒÍË ¯¬­¯ ÒÑ Ú°¯Ü°°Ë ²Ô ­Ë¸ Ôµ °y­±Ñ Íϸ Ò˶ÏÛÑÒÝ°ÏÞ ÒÑ ´Ð¹× Ó ´×¹Ð Ó ´Ð¹Ô Ø µÐ¹µ

¶¹

ʬ° ®°±¶°Ë¯­Ì° ÍÎ ¯¬° ®Í®ÛÏ­¯ÒÍË ÍÝ°± е °y­±Ñ Íϸ ÒÑ ´×¹Ð Ó ´Ð¹Ô Ó Ù¹Õ Ó ´²¹× Ø Ô´¹´

¸¹

ʬ° ®°±¶°Ë¯­Ì° Ï°ÑÑ ¯¬­Ë ²Ô °y­±Ñ Íϸ ÒÑ ²É¹É Ó Ô¹Õ Ó Ö¹× Ø ÐԹй ßÍ ¯¬°±° ­±° à¹ÐÔÐáà²ÕÔá Ø ÖÕ¹ÉÕÔ âÒÏÏÒÍË ®°Í®Ï° Ï°ÑÑ ¯¬­Ë ²Ô °y­±Ñ Íϸ¹

°¹

ãË °Ñ¯Òâ­¯° ÍÎ ¯¬° ËÛâÚ°± ÍÎ ±°¯Ò±°¸ ®°Í®Ï° ÒÑ à¹Ôáà¹ÉÙÕáà²ÕÔá Ó à¹´²×áà²ÕÔá Ø µ×¹×´²Ô âÒÏÏÒÍ˹

²´¹ ­·Ú¹

«Íâ®Û¯°± äÑ­Ì° àåÍÛ±Ñá É¹É ³ ²¹Ö Ð¹É ³ Ô¹Ö ×¹É ³ Ù¹Ö Ö¹É ³ ´´¹Ö ´²¹É ³ ´µ¹Ö Êͯ­Ï

æ±°ç۰˶y Ô ²Ù Ù × Ð ÔÉ

² ³ ´µ

è°Ï­¯ÒÝ° æ±°ç۰˶y ɹ´É ɹÔ× É¹´× ɹ´² ɹÉ× ´¹ÉÉ

éêëìíîïðîñê òðóðîëðîìëô õóö÷øóí óùú ûíóïüîìóø ýêðüþúë

ì

30 25

Frequency

20 15 10 5 0 0.0 - 2.9

3.0 - 5.9

6.0 - 8.9

9.0 - 11.9 12.0 - 14.9

Computer Usage (Hours) ú !



       









!



"





   

ê

õüê #ó$þíîð% þ& ðüê ìþ#ï÷ðêí ÷ëêíë óíê îù ðüê ' ðþ ( üþ÷í íóù)ê ðüê íî)üð +îðü ' ÷ëêíë îù ðüê
ÿ ðþ
 üþ÷í íóù)ê

ÿ




*ëó)ê

îë ëþ#ê+üóð ë,ê+êú ðþ+óíú

-./0123 4

448

4A8

4R8

9

:

;




?

?

9

;

>

?

@

9

9


B?s ?Ws t SB A?VX \rurur^ \turur^ \rurut^ \turut^ \rutur^ \tutur^ \rutut^ \tutut^

ZO |O

t>B TQAZTRBv ?CB BwQ?XXx XVyBXxu vT A>B @CTS?SVXVAx TU B?Z> TQAZTRBv Vv Nz{O }\~^ [ N z | UTC V [ Nu Fu ]u Du | }\~^  € UTC V [ Nu Fu ]u Du | }\~^ ‚ }\Eƒ^ ‚ }\E„^ ‚ }\E…^ ‚ }\E†^ [ N z | ‚ N z | ‚ N z | ‚ N z | ‚ N z | [ N t>B ZX?vvVZ?X RBA>Ts ‡?v QvBsO

DEF

ˆ‰Š‹ŒŽŠŒ‰ ŠŒ ‘‹Œ’“’”Š•

P›œž Ÿ š– ¡ ‘›œ¢ž Ÿ š£™¡ ‘›œ¤ž Ÿ š˜–

™š

¥¦§ ‹§”“Š¨§ ©‹§ªŽ§‰y«§Š¦Œ w “¬ Ž¬§š ®Œš ¯§ªŽ‹§«§‰Š ›–š˜ž ¬ ‰ŒŠ ¬“Š¬©§° Š¦§ ±‹Œ’“’”Š§¬ Œ ‰ŒŠ ¬Ž« ŠŒ ²š ‘›œ ž ³ ‘›E¢ž ³ ‘›E¤ž ³ ‘›E´ž Ÿ š²  ³ š²µ ³ š–  ³ š£  Ÿ š¶µ

­š ¶š

“š

¥¦§‹§ “‹§ ©ŒŽ‹ ŒŽŠŒ«§¬ ±Œ¬¬’”§ ©Œ‹ Š¦¬ £—¬Š§± §·±§‹«§‰Š° ±”“‰‰‰¸ Œ««¬¬Œ‰ ±Œ¬Š¨§ — ŒŽ‰” “±±‹Œ¨§¬° ±”“‰‰‰¸ Œ««¬¬Œ‰ ±Œ¬Š¨§ — ŒŽ‰” ¬“±±‹Œ¨§¬° ±”“‰‰‰¸ Œ««¬¬Œ‰ ‰§¸“Š¨§ — ŒŽ‰” “±±‹Œ¨§¬° ±”“‰‰‰¸ Œ««¬¬Œ‰ ‰§¸“Š¨§ — ŒŽ‰” ¬“±±‹Œ¨§¬š

’š

¹§Š

± Ÿ ±Œ¬Š¨§¡ ‰ Ÿ ‰§¸“Š¨§¡ “ Ÿ “±±‹Œ¨§¬¡ “‰  Ÿ ¬“±±‹Œ¨§¬ º»¼½½¾½¿ ÀÁ¾ÃþÁ½

CÁĽž» ¼

ÈÆÉ ¼Ê

Ç Æ

ÈÆÉ ÇÊ

½ ¼

.

È½É ¼Ê

Ç È½É ÇÊ

50I F 50! 50  49  48  47 G H4 JK 4!46!  4  3  2 1  230,300

˚ ² š “š

̬§ Š¦§ ‹§”“Š¨§ ©‹§ªŽ§‰• “±±‹Œ“¦Í ‘›C“”©Œ‹‰“ž Ÿ ²¡–˜–Σ¡˜­– Ÿ š™ 

’š

®Ž«’§‹ ‰ŒŠ ©‹Œ« – ¬Š“Š§¬ Ÿ £¡˜­– — ²¡–˜– — ˜Ë  — £²­ — ²²£ Ÿ ££² ‘›®ŒŠ ©‹Œ« – ϊ“Š§¬ž Ÿ ££²Î£¡˜­– Ÿ š Ë

š

‘›®ŒŠ ‰ E“‹”• ϊ“¸§¬ž Ÿ ² — š££ Ÿ š­¶

š

E¬Š«“Š§ Œ© ‰Ž«’§‹ Œ© Г¬¬“¦Ž¬§ŠŠ¬ Œ«±“‰§¬ ‰ §“‹”• ¬Š“¸§ Œ© §¨§”Œ±«§‰Š — ›š££ž˜Ë   ¶™

–—˜

ÑÒÓÔÕÖ× Ø ÖÚ

ÛÜ ÖwÓÝÝÞßÖ ÕÒÖ ÝàáÖ âÜ ÕÒÖ ÓÓw×ãÝ ãàã äâÕ ãàÜÜÖ× åyÝÕÓÕÖÝæ ÖwçÓä ßÞèÕàÔèé ÕÒÖ Ô×âåÓåàèàÕé Óä ÓÓw×ã ÖwäÕ Õâ Ñâèâ×Óãâ åyÕÒÖ ÕâÕÓè êÖäÕÞ×Ö ÜÞäãÝ ãàÝåÞ×ÝÖã Õâ ëÖÕ Óä ÖÝÕàßÓÕÖÚ ìÝÕàßÓÕÖ âÜ Ñâèâ×Óãâ ÜÞäãÝ í îïïðñðòóØôîõòðÚØô í õïÚöò åàèèàâä ÷ÞÕÒâ×Ýø ùâÕÖú ûÒÖ ÓçÕÞÓè ÓßâÞäÕ ëâàäë Õâ Câèâ×Óãâ üÓÝ $ïÚóØ åàèèàâäÚ

ïïÚ ÓÚ åÚ ïðÚ ÓÚ

ùâæ ÕÒÖ Ô×âåÓåàèàÕàÖÝ ãâ äâÕ ÝÞß Õâ âäÖÚ ûÒÖé ÝÞß Õâ ÚýöÚ þüäÖ× ßÞÝÕ ×ÖêàÝÖ ÕÒÖ Ô×âåÓåàèàÕàÖÝ Ýâ ÕÒÖé ÝÞß Õâ ïÚÿÿÚ ÝÖ ÕÒÖ çâÞäÕàäë ×ÞèÖ Üâ× çâßåàäÓÕàâäÝú

49I 49 ! F (49)(48)(47)(46)(45) G H5 JK 5!44!  (5)(4)(3)(2)(1)  1,906,884

åÚ


Ö×é ÝßÓèèú ïñïæÿæýýØ í ÿÚÿÿÿÿÿÿö

çÚ

ÞèÕàÔèé ÕÒÖ ÓäÝüÖ× Õâ ÔÓ×Õ îÓô åé Øð Õâ ëÖÕ ÕÒÖ äÞßåÖ× âÜ çÒâàçÖÝ Üâ× ÕÒÖ Ýà äÞßåÖ×ÝÚ ùâÚ âÜ CÒâàçÖÝ í îïæÿæýýØôîØðô í ýÿæÿýæïðý ×âåÓåàèàÕé âÜ àääàäë í ïñýÿæÿýæïðý í ÿÚÿÿÿÿÿÿÿïðö

IäàÕàÓèèé Ó Ô×âåÓåàèàÕé âÜ Úðÿ üâÞèã åÖ ÓÝÝàëäÖã àÜ ÝÖèÖçÕàâä àÝ ÖÞÓèèé èà ÖèéÚ DÓÕÓ ãâÖÝ äâÕ ÓÔÔÖÓ× Õâ çâäÜà×ß ÕÒÖ åÖèàÖÜ âÜ ÖÞÓè çâäÝÞßÖ× Ô×ÖÜÖ×ÖäçÖÚ Fâ× Ö ÓßÔèÖ ÞÝàäë ÕÒÖ ×ÖèÓÕàêÖ Ü×ÖÞÖäçé ßÖÕÒâã üÖ üâÞèã ÓÝÝàëä Ó Ô×âåÓåàèàÕé âÜ ö ñ ïÿÿ í Úÿö Õâ ÕÒÖ ãÖÝàëä ï âÞÕçâßÖæ Úïö Õâ ãÖÝàëä ðæ Úòÿ Õâ ãÖÝàëä òæ ÚØÿ Õâ ãÖÝàëä Øæ Óäã Úïÿ Õâ ãÖÝàëä öÚ

ïòÚ

ïØÚ ÓÚ

 îE ô í ï ñ Ø

åÚ

îÓäé ð âÞÕçâßÖÝô í ï ñ Ø  ï ñ Ø í ï ñ ð

çÚ

îÓäé ò âÞÕçâßÖÝô í ï ñ Ø  ï ñ Ø  ï ñ Ø í ò ñ Ø

ïöÚ ÓÚ

S í ÓçÖ âÜ çèÞåÝæ ÓçÖ âÜ ãàÓßâäãÝæ ÓçÖ âÜ ÒÖÓ×ÕÝæ ÓçÖ âÜ ÝÔÓãÖÝ}

åÚ

S í ð âÜ çèÞåÝæ ò âÜ çèÞåÝæ Ú Ú Ú æ ïÿ âÜ çèÞåÝæ âÜ çèÞåÝæ  âÜ çèÞåÝæ  âÜ çèÞåÝæ A âÜ çèÞåÝ}

çÚ

ûÒÖ×Ö Ó×Ö ïð Óç æ ÞÖÖäæ â× àäë àä ÖÓçÒ âÜ ÕÒÖ ÜâÞ× ÝÞàÕÝÚ

ãÚ

Fâ× Óú Ø ñ öð í ï ñ ïò í Úÿý Fâ× åú ïò ñ öð í ï ñ Ø í Úðö Fâ× çú ïð ñ öð í Úðò

ØÙØ

   #$% % &$' &$' ( )$ *+,- ,* %

89: /

89: .

.

/

0

1

2

3

.

/

0

1

2

3

4

/

0

1

2

3

4

5

0

1

2

3

4

5

6

1

2

3

4

5

6

.7

2

3

4

5

6

.7

..

3

4

5

6

.7

..

./

;? @@BF

>AGE

\W=3 Z9[8

>?@]

>B@C

>@?A

>DBF

>A?G

>DEE

>@GB

E>@@



I % ^ % _  %  `   %  !   % . ' % %  /  aa ,.

 b % . ' % %   . %   &% ^ ' % %  /  c*



(d |' ^)

cae f *a

+"



(d |/  ^)

c#e f "

"e*



F  /  - ` ^% .! (A)(B) F ^ . - (A  B)

(A)(B)

(A  B)

cae- (A)

(*a)(c*)

*a- (B)

c*

a*

,  (A)(B)  (A  B)- . ! %  

  /   " 

(g)

#"e h ##*



(i.)



( . i.)

#

##* h ##c h ##a h ##* (i.) (i.)

#a

(#a)(#a)

##cc



jklmnop q

uv

wxyznk {|} ~ wx{|} wx{|} ~ xtvt}xtvt} ~ tvtt€

ov

P(Rh- O) 

v

wx‚kƒ} ~ s r wx‚kr} ~ s r tvs ~ tv„

P(Rh-  O) .06   .136 P(O) .44

P(B Rh+)  …v lv

P(B  Rh+) .09   .106 P(Rh+) .85

wx†m zp ‡lˆ‰lpŠ} ~ …s ‹ q„ ~ tvŒqŒ

yv

wx†m zp olp} ~ …Œ ‹ q„ ~ tvŽ

v

wx†m zp olp  †m zp ‡lˆ‰lpŠ} ~ € ‹ q„ ~ tvŒtq wx†m zp olp |†m zp ‡lˆ‰lp Š} ~ tvŒtq ‹ tvŒqŒ ~ tv…

uv

‘koŠ lpo ˆzn ’ˆuomoˆuoˆn “’ˆo wx†m zp olp}  wx†m zp olp |†m zp ‡lˆ‰lpŠ} tvŽ  tv…

…Œv lv •‰mln’zˆ Cly’ˆon—l˜op ™lšŠop wkŠ“’l– ‘koplm’“n ”Š“no—“ Aˆl–Š“n

†ˆuop t vttt vst vttt vtt ‘znl– v€tt

tr vtt vtt vs€ vt€ v€t

”ln’“ln’zˆ ”zpo ŒtrŒ ŽtrŽ vstt vtŽ vt€ vt€ vtt vt€ vstt vtŽ v€Ž v€tt

yv

wx„t“} ~ vtŽ xl —lp›’ˆl– mpzyly’–’nŠ}

v

wx„t“ |w‘} ~ vtt‹v€t ~ v€t xl zˆu’n’zˆl– mpzyly’–’nŠ}

uv

wx™} ~ v€t xl —lp›’ˆl– mpzyly’–’nŠ}

ov

wx™  †ˆuop t} ~ vst xl œz’ˆn mpzyly’–’nŠ}

v

wx†ˆuop t |™} ~ vst‹v€t ~ vŒt xl zˆu’n’zˆl– mpzyly’–’nŠ}

›v

wxŽt zp k’›kop} ~ v€Ž x”‰— z —lp›’ˆl– mpzyly’–’n’o“}

…Žv lv

wxA  B} ~ wxA}wxB} ~ xv}xv…} ~ vs

yv

wxA  B} ~ wxA} ƒ wxB} r wxA  B} ~ v ƒ v… r vs ~ vŽs

v

wx“k‰nuzšˆ} ~ s r wxA  B} ~ s r vŽs ~ v€

q r st

„tr„ vt€ vttt vtt vttt vtŽ

‘znl– v€t v€t v€t v€t svttt

žŸ ¡¢£¤Ÿ¥¡ž Ÿ¡ ¦ ¡§¨§¥©¥Ÿª

®¯° ¨° §°

¤°

P(Telephone) 

52  0.2737 190

±²¥³ ¥³ ¨ž ¥žŸ´ ³´¤Ÿ¥¡ž ¡µ Ÿ¶¡ ´·´žŸ³° Ÿ ³´´¸³  ´¨³¡ž¨§©´ Ÿ¡ ¨³³£¸´ Ÿ²´ ž´ŸxŸ¶¡ ¸´³³¨¹´³ ¥w©© §´ ¥ž¢´º´ž¢´žŸ» ´w£³´ Ÿ²´ ¸£©Ÿ¥º©¥¤¨ Ÿ¥¡ž  £©´ µ¡  ¥ž¢´º´ž¢´žŸ ´·´žŸ³°

 30   15  ¦¼½¬¸¨¥©  ¾¨¿x À ¦¼½ ¬¸¨¥©¿ ¦¼¾¨¿x À     0.0125  190   190  ±²¥³ ¥³ ¨ £ž¥¡ž ¡µ Ÿ¶¡ ¸£Ÿ£¨©©ª ´¤x©£³¥·´ ´·´žŸ³° ¦¼±´©´º²¡ž´  žŸ´ ¡µµ¥¤´ Á¨¥©¿ À ¦¼±´©´º²¡ž´¿  ¦¼IžŸ´ ¡µµ¥¤´ Á¨¥©¿ À

®Ã° ¨° §°

52 18 70    0.7368 190 190 190

Ä´³Å ³¥ž¤´ ¦¼AÆ  AÇ¿ À È ¦¼AÆ  B¿ À ¦¼AÆ¿¦¼B | AÆ¿ À °«È¼°ÉÈ¿ À °È¯ ¦¼AÇ  B¿ À ¦¼AÇ¿¦¼B | AÇ¿ À °Êȼ°ÈË¿ À °È®

¤°

¦¼B¿ À ¦¼AÆ  B¿  ¦¼AÇ  B¿ À °È¯  °È® À °­­

¢°

P(A1 B) 

.08  .7273 .11

P(A 2 B) 

.03  .2727 .11

«È° ¨°

¦¼B  AÆ¿ À ¦¼AÆ¿¦¼B | AÆ¿ À ¼°ÉÈ¿ ¼°ËÈ¿ À °­È ¦¼B  AÇ¿ À ¦¼AÇ¿¦¼B | AÇ¿ À ¼°ËÈ¿ ¼°«È¿ À °ÉÈ ¦¼B  AÌ¿ À ¦¼AÌ¿¦¼B | AÌ¿ À ¼°®È¿ ¼°®È¿ À °ÈÃ

§°

P(A 2 B) 

.20  .51 .10  .20  .09

¤° Events A1 A2 A3

P(Ai) .20 .50 .30 1.00

P(B | Ai) .50 .40 .30

P(Ai  B) .10 .20 .09 .39

P(Ai | B) .26 .51 .23 1.00

ÍÆ À ³£¤¤´³³µ£©Å ÍÇ À ž¡Ÿ ³£¤¤´³³µ£© ¨ž¢ B À  ´Î£´³Ÿ  ´¤´¥·´¢ µ¡  ¨¢¢¥Ÿ¥¡ž¨© ¥žµ¡ ¸¨Ÿ¥¡ž°

«­° ¨°

¦¼ÍÆ¿ À °ËÈ

§°

¦¼B |Í Æ¿ À °ÏË

« ¬ ­­

ÐÑÒÓÔÕÖ ×

ÛÜ

P(S1 B) 

(.50)(.75) .375   .65 (.50)(.75)  (.50)(.40) .575

y ÕãÔ Ý Þ ßàááÕâ ÓÒß

×ÚÜ

äå Þ ÛæáÔçßÕÖ âÕèÒæéÔá äê Þ ÛæáÔçßÕÖ âçÕá ãçÔ âÕèÒæéÔ ëìäåí Þ Üîï

ëìäêí Þ Üðï

ëìÝ | Dêí Þ ÜÚ

P(D1 )P(M D1 )



ÒÜ

P(D1 M) 

ñÜ

òÕáó ÔÑÕ ÓÖçñÒñàéàÔô çè âÕèÒæéÔ àá õÖÕÒÔÕÖ ÔÑÒã ÜÚîÜ

×öÜ

P(D1 )P(M D1 )  P(D 2 )P(M D 2 )

ëìÝ | Dåí Þ Ù

(.05)(1) .05   .21 (.05)(1)  (.95)(.2) .24

÷ÕÔø ù Þ áßÒéé ÛÒÖ ùú Þ çÔÑÕÖ ÔôÓÕ çè ûÕÑàÛéÕ F Þ ÒÛÛàâÕãÔ éÕÒâá Ôç èÒÔÒéàÔô èçÖ ûÕÑàÛéÕ çÛÛæÓÒãÔ üÕ ÑÒûÕ ëìùí Þ ÜÙýó áç ëìùúí Þ ÜýÚÜ Aéáç ëìF |ùí Þ ÜÙÚý Òãâ ëìF |ù úí Þ ÜîïÜ þáàãõ ÔÑÕ ÔÒñæéÒÖ èçÖß çè BÒôÕá ÿÑÕçÖÕß ÓÖçûàâÕáø EûÕãÔá ù ùú

ëÖàçÖ ëÖçñÒñàéàÔàÕá ÜÙý ÜýÚ ÙÜîî

CçãâàÔàçãÒé ëÖçñÒñàéàÔàÕá ÜÙÚý Üîïî

çàãÔ ëÖçñÒñàéàÔàÕá ÜîÚö Üî×Ù Üî
×

ëçáÔÕÖàçÖ ëÖçñÒñàéàÔàÕá Üö
Ü
× ÙÜîî

FÖçß ÔÑÕ ÓçáÔÕÖàçÖ ÓÖçñÒñàéàÔô Ûçéæßãó Õ ÑÒûÕ ëìù | F í Þ Üö
Ü ùçó àè Òã ÒÛÛàâÕãÔ éÕÒâá Ôç Ò èÒÔÒéàÔôó ÔÑÕ ÓÖçñÒñàéàÔô Ò áßÒéé ÛÒÖ Òá àãûçéûÕâ àá Üö
Ü

××Ü

÷ÕÔ

Aå Þ ùÔçÖô ÒñçæÔ BÒáÕÔñÒéé ÿÕÒß Aê Þ ùÔçÖô ÒñçæÔ HçÛÕô ÿÕÒß ü Þ "üÕ üàã" ÑÕÒâéàãÕ

ëìAåí Þ Ü
î

ëìü | Aåí Þ Ü
×Ù

ëìAêí Þ Ü×î

ëìü | Aêí Þ Ü×
Ú

A Aå Aê

ëìAí Ü
î Ü×î

ëìü | Aåí Ü
×Ù Ü×
Ú

ëìü  Aí Üöý×
ÜÙý×ý Üï
ð×

ëìA |Ý í Üöý×
Üï
ð× ÜÙý×ýÜï
ð×

ÿÑÕ ÓÖçñÒñàéàÔô ÔÑÕ áÔçÖô àá ÒñçæÔ ÔÑÕ ñÒáÕÔñÒéé ÔÕÒß àá Ü
ï×Ü ×ïÜ ÒÜ Events D1 D2

P(Di) .60 .40 1.00

P(S1 | Di) P(Di  S1) .15 .090 .80 .320 P(S1) = .410

ëìDå |ù åí Þ ÜÚÙðï

× Ø ÙÚ

P(Di | S1) .2195 .7805 1.000

Þ Ü
ï× Þ ÜöÚ×
ÙÜîîîî

       

 |   !"#$ 

Events D1 D2

P(S2 | Di) P(Di  S2) .10 .060 .15 .060 P(S2) = .120

P(Di) .60 .40 1.00

P(Di | S2) .500 .500 1.000

D |   $# D |   $# 

Events D1 D2

P(Di) .60 .40 1.00

D | %  ""&

P(S3 | Di) P(Di  S3) .15 .090 .03 .012 P(S3) = .102

P(Di | S3) .8824 .1176 1.0000

D | %  !'

()* +* ,) *  ,  *) - . ,  ) +* ,  ,  *) +* *

Events D1 D2

P(Di) .2195 .7805 1.0000

P(S2 | Di) .10 .15

P(Di  S2) .0220 .1171 .1391

P(Di | S2) .1582 .8418 1.0000

D |     $"& D |     "" '



E/**   "  *  G   $#  *  1 *2



G  E/**  

" 0 $#  '"

E3* )  * .  */ )3* )*  ,* ) .  +)* *  4

#$  #$  $ !$ 5* *) . * $& *), * )  * ( .,*) ,



#$  #  # $ 5* *) . * # *), * )   67    )7*

!



& &  



8*

)  ) *))- 

 ) *))- 

  

9:;? @

CDE

FGHIJ

s

KL

u

s

KM

u

s

KN

u KO PQ

R S T EU V

EW}

X S TE U V

EY}

ZQ

R

X

S T EU V

>Q

R

X

S T EU }

[Q

\]^ _`aP> R

@dQ ;Q

EWV EY}

 X :;_ ; _;b Zg S hQiB

jQ

k:> Bd A l@ m>;? ]cZ n?]o< fi@% _;=`_[`>Zg ;aZ =:> ip ;aZ ]q>? n?]o< frh% _;=`_[`>ZgQ

PQ

efa]= _;=`_[`>Zg S hQsi t hQh@ S hQlh

@uQ

v>=

I S =?>;=b>a=AP;o_>Z `awo?m D S Z>;=: [?]b `awo?m \ S `awo?m P;o_>Z jm a>nc`n>aP> X S b;c n`q>a efIg S hQh@V ef\ ;aZ ef$ |Xg S hQph ;Q

ef\g S ef\

| gI S hQspV

efD

| gI S ByrV

| gI efIg t ef\ | Izg efIzg

S fhQspgfhQh@g t fhgfhQuig S hQhB

@ A B@

efX |\g S ByrQp S hQBlllV

{|}~€‚}ƒ| } „~…†…ƒ‡ƒ}ˆ

… „Ž

‘ „Ž

| I „ŽI ’ „ŽD | I“ „ŽI“

‘ Ž‹”•Ž––‰ ’ Ž–Ž–—˜ ‘ –––˜ ‚

“ “ „Ž™ ‘ „Ž™ |š „Žš ’ „Ž™ |š  „Žš  ‘ Ž–‹›››Ž––‹ ’ Ž–Ž–—— ‘ –––‹››› „Ž$

‘ „Ž$ |™ „Ž™ ’ „Ž$

| ™“ „Ž™“

‘ Ž–ŒŽ–––‹››› ’ Ž–Ž–——œ• ‘ ––––˜• Œ– †

„~…†…ƒ‡ƒ}ˆ  }žŸ Ÿ Ÿ|}

‘ „Ž† Ÿ~†¡Ÿ ’ „Ž†… Ÿ † Ÿ~†¡Ÿ ’ „ŽŸ¢‚Ÿ‡‡Ÿ|}

‘

11 14 13   50 50 50

‘ ££ ’ £œ ’ £˜ ‘ •˜ …

„~…†…ƒ‡ƒ}ˆ  }žŸ Ÿ Ÿ|}

‘ „Ž¤~ ’ „Ž…Ÿ‡¥ † Ÿ~†¡Ÿ

‘

Œ‹ †

4 8  .24 50 50

„Ž‡Ÿ†¦Ÿ¦ ‹ ‘ ‹˜œ ” —›£ ‘ –‹œ

…

„Ž£ ~ Ÿ¥Ÿ~ ‘ ‰–‹ ” —›£ ’ £‰£ ” —›£ ’ ˜Œ ” —›£ ‘ •–œ ” —›£ ‘ –•˜

‚

„Ž› ~ §~Ÿ ‘ ‹œ˜ ” —›£ ’ ‹‹£ ” —›£ ‘ £—œ ” —›£ ‘ –›£

€

„Ž| ‚†~¦ ‘ ‹— ” —›£ ‘ ––£

Œ£ †

‰ Š ‹Œ

¨©ª«¬­® ¯

³´µ

¶·

˷̺Í

¸¹ º»¼ ½»¼´¾

ÈÄøÁ

ÈÃÊÊÁ

ȸø¸

¸¿ À ¸Á

ÈĿɸ

ÈÄÉÂÉ

ȹ¹ÁÃ

¸Â À ¹Ã

ÈÃÊÄÂ

ÈŸÉ

ȸ¸¿Å

¹Ä À ¹Å

Èù¸Â

ÈÃÊÅÁ

Èĸɹ

¹Á º»¼ ÆÇ´¾

ÈøŹ

ÈÃɹÂ

ÈÄÃÊÃ

˷̺Í

È¿ÃÃÅ

ÈÅÊÊÅ

ÄÈÃÃÃÃ

ÎÏ

ÏÐÑÐÐ

ÒÏ

ÏÐÐ¯Ó Ô Ï±ÐÕÖ Ô Ï±Ñ×Ñ Ø Ï¯²±Õ

ÙÏ

ϯÑÑÓ

ÓÖÏ ªÏ

ÚÛЯ ¬Ü в |Ý­Þß Ø Ï±¯ÕÐ à ϯÑÑÓ Ø ÏÖáÑÑ

ÎÏ

ÚÛÝ­Þ |Ö² ªâÙ Üã­®ß Ø ÏÑÐÓÖ à ϱÑ×Ñ Ø ÏÐÖб

ÒÏ

ϱÑв Ô Ï±¯ÕÐ Ô Ï±ÕáÕ Ô ÏÑ×±á Ô ÏÑÖÐá Ô ÏÑÐÓÖ Ø ÏÓÕÕÖ

ÙÏ

ÚÛÖ± Ü® äÜ®­ |åÜß Ø ÛÏÑ×Ó² Ô ÏÑÕÖáß à ÏÓ××Ó Ø ÏÐ××±

­Ï

åÜæ έҪçÞ­ ¬©­ ÒÜâÙè¬èÜâªé «®ÜΪÎèéè¬è­Þ ÙÜ âܬ ªéé ­êçªé ¬©­ 䪮ëèâªé «®ÜΪÎèéè¬è­ÞÏ ÚÛЯ ¬Ü в |Ý­Þß Ø ÏÖáÑÑ ì­¬

Ó¯Ï

.

I



ÚÛЯ ¬Ü Ð²ß Ø ÏÖÖ²Ñ

Ø èä«Ü®¬ªâ¬ Ü® ã­®í èä«Ü®¬ªâ¬

î Ø äªé­

F

Ø ï­äªé­

ªÏ

ÚÛIß Ø Ï¯× Ûª 䪮ëèâªé «®ÜΪÎèéè¬íß

ÎÏ

ÚÛI |îß Ø ÏÐÐàÏÓÑ Ø Ï¯¯ Ûª ÒÜâÙè¬èÜâªé «®ÜΪÎèéè¬íß

ÒÏ

ÚÛI

ÙÏ

I¬ èÞ âܬ èâÙ­«­â٭⬠ªâÙ

|F ß Ø ÏÐáàÏÓÑ Ø ÏÓ¯ Ûª ÒÜâÙè¬èÜâªé «®ÜΪÎèéè¬íß

ÚÛIß Ø Ï¯×

 ÚÛI |îß Ø Ï¯¯

ÚÛIß Ø Ï¯×

ß Ø ÏÓ¯  ÚÛI | F

¯ ° ±²

FÜ® èâÞ¬ªâÒ­æ

ðñòóôõö÷òøôñ òô ùóôúûúøüøòý





û

øñ÷ üü ô øôóòûñ÷ ø õñõñò ôñ ñõó w÷ôñ÷üöõ ò ûò ûü ûñõ ûü ó ôñõñò û õøóñò ûòòøòöõ òôûwóõ óø 

P(B S) 

P(B  S) .12   .30 P(S) .40

 û ù | >

ùB

  ÷ôñòøñö ò  ûõ øñ÷ øò øñ÷óû  ò  óôúûúøüøòý ô û öó÷ û  ú

÷

E òøûò ò  ÷ôûñý ûó ò ûó ûò % Côñòøñöøñ ò  ûõóòø ñò ôöüõ øñ÷óû  ò  ûó ò ûó øñ÷ ùB |  

P(B S) 

P(B  S) .10   .333 P(S) .30

  ÷ôñõ ûõ û û úø

ó ÷ò 

û

ùA

ú

ù  B ù A

      B     

õ

ù A

| B  ùA  B  ùB         



ô ùA | B 

÷




   

ùA

A  üô ò òø û÷÷øõñò øñ ÷öóóñò ýûó B  üô ò òø û÷÷øõñò óøôö ýûó

ò

Gøñ

ù  B

  ùA   ùA | B   

û

ù A

 B 

ù A

ú

ù A

 B 

ùA

  

 

ò

| BùB      ù B  ÿ ù A

 B

 ÿ    

ôó

 %

A  óòöóñ ø óûöõöüñò B  !÷õ I" òûñõûóõ ôó õõö÷òøôñ

Gøñ ùA | B   ùA | B#   ùB   øñõ ùA   ôò ùB#  ÿ ùB   ùA

 ù  A  B ù  A  B #   ùBùA | B ùB #ùA | B#     þþ

  òøûò þþ% $øüü ú óûöõöüñò 

û

ù%øü

 

  


ú

ò   ôøü ò ò ó öüò

þÿ




&'()*+, -

Events High Quality (A1) Medium Quality (A2) No Oil (A3)

P(Ai) .50 .20 .30 1.00

P(S | Ai) .20 .80 .20

P(Ai  S) .10 .16 .06 P(S) = .32

P(Ai | S) .31 .50 .19 1.00

123456 7 80/ 'w49' 4: ;