A Primer in Probability, Second Edition

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CRC Press, Jul 27, 1990 - Mathematics - 336 pages
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Somewhat revised/expanded new edition of a problem-oriented introductory undergraduate text, the first edition of which appeared about a decade ago. The author writes with courteous clarity, and imposes only modest demands upon the mathematical skills of her readers. Problems at the end of each of t
 

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Contents

A First Glimpse of Probability
1
DETERMINISTIC OR RANDOM
3
14 INTERPRETING PROBABILITY
4
PROBLEMS
6
Basic Concepts of Probability
9
22 EVENTS AND THEIR PROBABILITIES
10
23 COMBINING EVENTS
12
24 PROBABILITIES ASSOCIATED WITH COMBINED EVENTS
14
PROBLEMS
132
Describing the Joint Behavior of Several Random Variables
139
82 COVARIANCE
140
83 EXPECTATION OF THE SUM OF SEVERAL RANDOM VARIABLES
144
84 VARIANCE OF THE SUM OF SEVERAL RANDOM VARIABLES
145
85 CORRELATION COEFFICIENT
148
86 PROBLEMS CONCERNING SEVERAL RANDOM VARIABLES
150
87 RANDOM VARIABLES BASED ON SAMPLES
155

25 FINDING PROBABILITIES
20
PROBLEMS
23
Counting Procedures and Their Applications in Computing Probabilities
31
32 COUNTING PROCEDURES INVOLVING ORDER RESTRICTIONS
33
33 COUNTING PROCEDURES NOT INVOLVING ORDER RESTRICTIONS
36
34 APPLICATIONS OF COUNTING PROCEDURES
37
ROLE OF DISTINGUISHABILITY
43
36 RANDOM SAMPLING
46
PROBLEMS
51
Conditional Probability
59
42 MULTIPLICATION RULE AND ASSIGNING PROBABILITIES
65
43 STAGEWISE EXPERIMENTS
67
BAYES RULE
70
PROBLEMS
74
Independence
81
52 INDEPENDENCE FOR MORE THAN TWO EVENTS
85
53 PROBABILITIES ASSOCIATED WITH MUTUALLY INDEPENDENT EVENTS
86
PROBLEMS
91
Random Variables
97
62 CUMULATIVE DISTRIBUTION FUNCTION
103
63 FUNCTIONS OF A RANDOM VARIABLE
106
64 JOINT PROBABILITY FUNCTIONS
107
65 MARGINAL PROBABILITY FUNCTIONS
109
66 INDEPENDENCE
110
PROBLEMS
113
Describing Random Variables and Their Distributions
121
72 LAWS OF EXPECTATION FOR A SINGLE RANDOM VARIABLE
125
73 VARIANCE
126
74 LAWS OF VARIANCE FOR A SINGLE RANDOM VARIABLE
130
75 STANDARDIZED RANDOM VARIABLES
131
PROBLEMS
158
Special Discrete Probability Models
165
92 WAITING TIME DISTRIBUTIONS
171
93 POISSON DISTRIBUTION
176
94 HYPERGEOMETRIC DISTRIBUTION
180
95 SUMS OF BINOM1AL RANDOM VARIABLES
186
96 MULTINOMIAL DISTRIBUTION
191
PROBLEMS
194
Statistical Inference
201
102 TESTING FOR GOODNESS OF FIT
205
103 TESTS FOR COMPARING TWO GROUPS
209
PROBLEMS
211
Continuous Distributions
217
112 NORMAL DISTRIBUTION
219
PROBLEMS
225
Limit Theorems
229
122 LAW OF LARGE NUMBERS
232
123 CENTRAL LIMIT THEOREM
233
124 APPROXIMATING DISCRETE DISTRIBUTIONS USING THE CENTRAL LIMIT THEOREM
234
PROBLEMS
245
Summation and Subscripts
249
Set Theory
253
Mathematical Induction as a Method of Proof
257
Binomial Expansions
261
Infinite Series
267
Tables
271
Answers to Selected Problems
285
Index
315
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