A first course in probability models and statistical inference:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1994
|
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXI, 717 S. graph. Darst. |
| ISBN: | 3540941142 0387941142 |
Staff View
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| 100 | 1 | |a Creighton, James H. C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first course in probability models and statistical inference |c J. H. C. Creighton |
| 264 | 1 | |a New York u.a. |b Springer |c 1994 | |
| 300 | |a XXXI, 717 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
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| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 7 | |a Statistique mathématique |2 ram | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Mathematical statistics | |
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CONTENTS
STUDENT
'
S
INTRODUCTION
.
VII
INSTRUCTOR
'
S
INTRODUCTION
.
XI
ACKNOWLEDGMENTS
.
XXV
CHAPTER
1
-
INTRODUCTION
TO
PROBABILITY
MODELS
OF
THE
REAL
WORLD
2
1.1
PROBABILITY
DISTRIBUTIONS
OF
RANDOM
VARIABLES
.
3
PROBABILITY
MODELS
.
3
RANDOM
VARIABLES
AND
THEIR
RANDOM
EXPERIMENTS
.
5
1.2
PARAMETERS
TO
CHARACTERIZE
A
PROBABILITY
DISTRIBUTION
.
11
THE
EXPECTED
VALUE
OR
MEAN
OF
A
RANDOM
VARIABLE
.
11
THE
VARIANCE,
MEASURING
THE
ACCURACY
OF
THE
MEAN
.
14
1.3
LINEAR
FUNCTIONS
OF
A
RANDOM
VARIABLE
.
20
1.4
THE
FUNDAMENTALS
OF
PROBABILITY
THEORY
.
23
THREE
BASIC
RULES
OF
PROBABILITY
.
23
BAYES
'
THEOREM
.
25
RANDOM
EXPERIMENTS
WITH
EQUALLY
LIKELY
OUTCOMES
.
28
CHEBYSHEV
'
S
THEOREM
.
30
1.5
SOME
REVIEW
EXERCISES
.
32
XXVIII
CONTENTS
CHAPTER
2
-
UNDERSTANDING
OBSERVED
DATA
38
2.1
OBSERVED
DATA
FROM
THE
REAL
WORLD
.
39
PRESENTING
DATA
GRAPHICALLY
.
39
COLLECTING
DATA
.
42
SIMPLE
RANDOM
SAMPLES
DRAWN
FROM
A
PROBABILITY
DISTRIBUTION
.
46
POPULATIONS
.
49
STATISTICAL
QUESTIONS
.
51
SIMPLE
RANDOM
SAMPLES
DRAWN
FROM
A
POPULATION
.
54
2.2
PRESENTING
AND
SUMMARIZING
OBSERVED
NUMERIC
DATA
.
61
MEASURES
OF
CENTRALITY
FOR
OBSERVED
NUMERIC
DATA
.
61
MEASURES
OF
SPREAD
FOR
OBSERVED
NUMERIC
DATA
.65
2.3
GROUPED
DATA:
SUPPRESSING
IRRELEVANT
DETAIL
.68
GROUPED
DISTRIBUTIONS
OF
OBSERVED
REAL
WORLD
DATA
.
68
HISTOGRAMS:
GRAPHICAL
DISPLAY
OF
GROUPED
RELATIVE
FREQUENCY
DISTRIBUTIONS
.
71
2.4
USING
THE
COMPUTER
.
74
DESCRIBING,
PICTURING,
AND
COMPARING
POPULATION
AND
SAMPLE
DATA
.
74
CHAPTER
3
-
DISCRETE
PROBABILITY
MODELS
80
3.1
INTRODUCTION
.
81
3.2
THE
DISCRETE
UNIFORM
DISTRIBUTION
.
81
3.3
THE
HYPERGEOMETRIC
DISTRIBUTION
.
83
COUNTING
RULES
.
83
WHAT
IS
THE
HYPERGEOMETRIC
MODEL
.
85
CALCULATING
THE
PROBABILITIES
.
87
THE
FORMULAS
.89
3.4
SAMPLING
WITH
REPLACEMENT
FROM
A
DICHOTOMOUS
POPULATION
.93
WHAT
IS
THE
MODEL?
.
93
THE
FORMULAS
.95
3.5
THE
BERNOULLI
TRIAL
.
97
3.6
THE
GEOMETRIE
DISTRIBUTION
.98
WHAT
IS
THE
MODEL?
.
98
THE
FORMULAS
.
100
CONTENTS
XXIX
3.7
THE
BINOMIAL
DISTRIBUTION
.
104
THE
BINOMIAL
EXPERIMENT
.
104
THE
BINOMIAL
RANDOM
VARIABLE
ITSELF
.
107
3.8
THE
POISSON
DISTRIBUTION
.110
3.9
THE
NEGATIVE
BINOMIAL
DISTRIBUTION
.116
3.10
SOME
REVIEW
PROBLEMS
.120
CHAPTER
4
-
CONTINUOUS
PROBABILITY
MODELS
128
4.1
CONTINUOUS
DISTRIBUTIONS
AND
THE
CONTINUOUS
UNIFORM
DISTRIBUTION
.129
CONTINUOUS
DISTRIBUTIONS
.129
THE
PROBABILITY
DENSITY
FUNCTION
.130
THE
CONTINUOUS
UNIFORM
DISTRIBUTION
.
132
4.2
THE
EXPONENTIAL
DISTRIBUTION
.
135
MODELING
THE
RELIABILITY
OF
A
SYSTEM
.
135
THE
EXPONENTIAL
DISTRIBUTION
.
136
4.3
THE
NORMAL
DISTRIBUTION
.
140
THE
NORMAL
DISTRIBUTION
AS
A
MODEL
FOR
MEASUREMENT
ERROR
.
140
THE
NORMAL
DISTRIBUTION
AS
AN
ABSTRACT
MODEL
.
147
THE
STANDARDIZING
TRANSFORMATION
.
151
THE
NORMAL
PROBABILITY
PLOT
.
154
CONTINUOUS
APPROXIMATIONS
TO
INTEGER-VALUED
RANDOM
VARIABLES
.
156
THE
NORMAL
APPROXIMATION
TO
THE
BINOMIAL
.159
4.4
THE
CHI-SQUARED
DISTRIBUTION
.
161
4.5
A
FEW
REVIEW
PROBLEMS
.
163
CHAPTER
5
-
ESTIMATION
OF
PARAMETERS
168
5.1
PARAMETERS
AND
THEIR
ESTIMATORS
.
169
INTRODUCTION
.
169
ESTIMATORS
THE
ENTIRE
CONTEXT
.
173
5.2
ESTIMATING
AN
UNKNOWN
PROPORTION
.
176
THE
SAMPLING
DISTRIBUTION
FOR
P
.
176
ESTIMATING
THE
VALUE
OF
AN
UNKNOWN
P
.
180
CONSTRUCTING
THE
CONFIDENCE
INTERVAL
FOR
P
.184
XXX
CONTENTS
THE
EXACT
(ALMOST)
ENDPOINTS
OF
A
CONFIDENCE
INTERVAL
FOR
P
.
189
A
LESS
CONSERVATIVE
APPROACH
TO
THE
STANDARD
ERROR
FOR
P
.
.
190
TOO
MANY
APPROXIMATIONS:
ARE
THEY
VALID?
.
193
THE
APPROPRIATE
SAMPLE
SIZE
FOR
A
GIVEN
ERROR
TOLERANCE
.
194
5.3
ESTIMATING
AN
UNKNOWN
MEAN
.
196
THE
ESTIMATOR
X
.
196
THE
CENTRAL
LIMIT
THEOREM
.
197
THE
SAMPLING
DISTRIBUTION
FOR
X
.
199
CONSTRUCTING
A
CONFIDENCE
INTERVAL
FOR
P
.
200
ESTIMATING
THE
STANDARD
ERROR
(ER/
Y/N
S/Y/N),
USING
S
INSTEAD
OF
ER
TAKES
US
TO
STUDENT
'
S
^DISTRIBUTION
WHEN
THE
DISTRIBUTION
YOU
'
RE
SAMPLING
FROM
IS
NORMAL
.
208
5.4
A
CONFIDENCE
INTERVAL
ESTIMATE
FOR
AN
UNKNOWN
ER
.
214
5.5
ONE-SIDED
INTERVALS,
PREDICTION
INTERVALS,
TOLERANCE
INTERVALS
.
217
ONE-SIDED
CONFIDENCE
INTERVALS
.
217
PREDICTION
INTERVALS
FOR
OBSERVATIONS
FROM
A
NORMAL
DISTRIBUTION
.
218
TOLERANCE
INTERVALS
.
221
CHAPTER
6
-
INTRODUCTION
TO
TESTS
OF
STATISTICAL
HYPOTHESES
224
6.1
INTRODUCTION
.
225
STATISTICAL
HYPOTHESES
.
225
WHAT
ARE
THESE
TWO
TESTING
PROCEDURES?
.
227
CONTRASTING
THE
TWO
TESTING
PROCEDURES
.
229
6.2
TESTS
OF
SIGNIFICANCE
.
231
A
DIALOGUE
.
232
THE
P-VALUE
.
234
COMPARING
MEANS
AND
COMPARING
PROPORTIONS
(LARGE
SAMPLES):
TWO
NEW
PARAMETERS
AND
THEIR
ESTIMATORS
.
237
PRACTICAL
VERSUS
STATISTICAL
SIGNIFICANCE
.
241
THE
TEST
OF
SIGNIFICANCE
AS
AN
ARGUMENT
BY
CONTRADICTION
.
242
WHAT
IF
THE
P-VALUE
IS
NOT
SMALL?
.
243
A
CASE
WHERE
"
NOT
SMALL
P-VALUE
"
IS
CONCLUSIVE
AND
"
SMALL
"
NOT
.
245
CONTENTS
XXXI
CHI-SQUARED
TESTS
FOR
GOODNESS
OF
FIT,
HOMOGENEITY,
AND
INDEPENDENCE
.
249
6.3
HYPOTHESIS
TESTS
.
254
INTRODUCTION
.
254
SETTING
UP
THE
HYPOTHESIS
TEST
.
256
THE
POSSIBLE
ERRORS
.
259
REAL-WORLD
INTERPRETATION
OF
THE
CONCLUSIONS
AND
ERRORS
.
263
MOVING
IN
THE
DIRECTION
OF
COMMON
PRACTICE
.
265
THE
REJECTION
REGION
.
268
THE
DECISION
RULE
AND
TEST
STATISTIC
.
269
P-VALUES
FOR
HYPOTHESIS
TESTS
.
273
CONTROLLING
POWER
AND
TYPE
II
ERROR
.
274
6.4
A
SOMEWHAT
COMPREHENSIVE
REVIEW
.
279
CHAPTER
7
-
INTRODUCTION
TO
SIMPLE
LINEAR
REGRESSION
288
7.1
THE
SIMPLE
LINEAR
REGRESSION
MODEL
.
290
7.2
THE
LEAST
SQUARES
ESTIMATES
FOR
A
AND
SS
.
295
THE
PRINCIPLE
OF
LEAST
SQUARES
.
297
CALCULATING
THE
LEAST
SQUARES
ESTIMATE
OF
A
AND
SS
.
300
7.3
USING
THE
SIMPLE
LINEAR
REGRESSION
MODEL
.
305
TESTING
HYPOTHESES
CONCERNING
SS
.
308
THE
COEFFICIENT
OF
DETERMINATION
.311
CONFIDENCE
INTERVALS
TO
PREDICT
HY
\
X
OR
THE
AVERAGE
OF
A
FEW
Y
'
S
FOR
X
P
,
A
PARTICULAR
VALUE
OF
X
.
317
7.4
SOME
REVIEW
PROBLEMS
.
321
THE
DATA
.321
ANSWERS
TO
TRY
YOUR
HAND
-
LEVEL
1
.
326
ANSWERS
TO
TRY
YOUR
HAND
-
LEVEL
II
.
442
TABLES
.
702
THE
STANDARD
NORMAL
DISTRIBUTION
.
703
STUDENT
'
S
I-DISTRIBUTION
.
704
THE
CHI-SQUARED
DISTRIBUTION
.
705
BIBLIOGRAPHY
.
707
INDEX
OF
NOTATION
.
709
AUTHOR
INDEX
.
711
SUBJECT
INDEX
.
713 |
| any_adam_object | 1 |
| author | Creighton, James H. C. |
| author_facet | Creighton, James H. C. |
| author_role | aut |
| author_sort | Creighton, James H. C. |
| author_variant | j h c c jhc jhcc |
| building | Verbundindex |
| bvnumber | BV009524657 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.C847 1994 |
| callnumber-search | QA273.C847 1994 |
| callnumber-sort | QA 3273 C847 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 800 SK 820 |
| classification_tum | MAT 600f MAT 620f |
| ctrlnum | (OCoLC)605103473 (DE-599)BVBBV009524657 |
| dewey-full | 519.5 519.520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 519.5 20 |
| dewey-search | 519.5 519.5 20 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009524657 |
| illustrated | Illustrated |
| indexdate | 2024-08-18T00:19:48Z |
| institution | BVB |
| isbn | 3540941142 0387941142 |
| language | English |
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| oclc_num | 605103473 |
| open_access_boolean | |
| owner | DE-824 DE-12 DE-91 DE-BY-TUM DE-703 DE-739 DE-19 DE-BY-UBM DE-20 DE-521 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-824 DE-12 DE-91 DE-BY-TUM DE-703 DE-739 DE-19 DE-BY-UBM DE-20 DE-521 DE-634 DE-83 DE-11 DE-188 |
| physical | XXXI, 717 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Creighton, James H. C. Verfasser aut A first course in probability models and statistical inference J. H. C. Creighton New York u.a. Springer 1994 XXXI, 717 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Probabilités ram Statistiek gtt Statistique mathématique ram Waarschijnlijkheidstheorie gtt Statistik Probabilities Mathematical statistics Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 s DE-604 Stochastisches Modell (DE-588)4057633-4 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006289340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Creighton, James H. C. A first course in probability models and statistical inference Probabilités ram Statistiek gtt Statistique mathématique ram Waarschijnlijkheidstheorie gtt Statistik Probabilities Mathematical statistics Stochastisches Modell (DE-588)4057633-4 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4182963-3 |
| title | A first course in probability models and statistical inference |
| title_auth | A first course in probability models and statistical inference |
| title_exact_search | A first course in probability models and statistical inference |
| title_full | A first course in probability models and statistical inference J. H. C. Creighton |
| title_fullStr | A first course in probability models and statistical inference J. H. C. Creighton |
| title_full_unstemmed | A first course in probability models and statistical inference J. H. C. Creighton |
| title_short | A first course in probability models and statistical inference |
| title_sort | a first course in probability models and statistical inference |
| topic | Probabilités ram Statistiek gtt Statistique mathématique ram Waarschijnlijkheidstheorie gtt Statistik Probabilities Mathematical statistics Stochastisches Modell (DE-588)4057633-4 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Probabilités Statistiek Statistique mathématique Waarschijnlijkheidstheorie Statistik Probabilities Mathematical statistics Stochastisches Modell Statistische Schlussweise |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006289340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT creightonjameshc afirstcourseinprobabilitymodelsandstatisticalinference |