TOPIC
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TEXT
BY MILLER & MILLER
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HOMEWORKS
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CHAPTER 1. INTRODUCTION
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Counting Techniques
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§ 1.1-1.3
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Pg. 17-24
1.6, 1.7, 1.24,
1.25, 1.28, 1.31, 1.34, 1.35, 1.36, 1.40, 1.43, 1.49, 1.53, 1.54
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CHAPTER 2. PROBABILITY
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Introduction & Sample
Space and Events
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§ 2.1, 2.2, 2.3
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Pg. 32-36
2.4, 2.6, 2.10,
2.12, 2.14, 2.20, 2.22
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Probabilities &
Rules of Probability
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§ 2.4-2.5
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Pg. 46-52
2.25, 2.27, 2.31, 2.33,
2.34, 2.36, 2.39, 2.42, 2.47, 2.53, 2.55, 2.56
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Conditional Probabilities
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§ 2.6
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Pg. 65-72
2.64, 2.69, 2.75,
2.76, 2.83, 2.88, 2.91, 2.98, 2.99, 2.104
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Independent Events
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§ 2.7
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Bayes' Formula
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§ 2.8
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CHAPTER 3. PROBABILITY
DISTRIBUTIONS & DENSITIES
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Random Variables
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§ 3.1
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Pg. 86-89
3.2, 3.4, 3.11, 3.12,
3.20, 3.21
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Discrete Random Variables
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§ 3.2
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Continuous Random Variables
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§ 3.3-3.4
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Pg. 97-101
3.37, 3.38, 3.40, 3.41,
3.51, 3.53, 3.55
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Multivariate Distributions
(Jointly Distributed Random Variables)
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§ 3.5
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Pg. 111-115
3.56, 3.57, 3.63, 3.76.
3.77, 3.85, 3.87
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Marginal & Conditional
Distributions
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§ 3.6, 3.7
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Pg. 125-128
3.89, 3.90, 3.94, 3.105,
3.108
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TOPIC
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TEXT BY MILLER &
MILLER
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HOMEWORKS
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CHAPTER 4. EXPECTATION
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Expectation of a Random
Variable, Moments, Chebyshev's Theorem
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§ 4.1, 4.2, 4.3,
4.4
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Pg. 137-140
4.6, 4.8, 4.9, 4.19,
4.20
Pg. 149-153
4.27, 4.34, 4.39, 4.43,
4.48, 4.54
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Moment Generating Functions
Product Moments
Moments of Linear Combinations
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§ 4.5, 4.6, 4.7
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Pg. 163-166
4.64, 4.65, 4.69, 4.78,
4.80
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Conditional Expectation
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§ 4.8
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CHAPTER 5. DISCRETE
PROBABILITY DISTRIBUTIONS
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Introduction & Discrete
Uniform
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§ 5.1, 5.2
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Pg. 175-180
5.5, 5.16, 5.19,
5.26, 5.27
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Bernoulli & Binomial
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§ 5.3, 5.4
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Negative Binomial &
Geometric
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§ 5.5
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Pg. 192-198
5.39, 5.46, 5.55,
5.58, 5.61, 5.72, 5.78
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Hypergeometric
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§ 5.6
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Poisson
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§ 5.7
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Multinomial
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§ 5.8
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Pg. 201-202
5.84, 5.87
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Multivariate Hypergeometric
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§ 5.9
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CHAPTER 6. CONTINUOUS
PROBABILTY DISTRIBUTIONS
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Introduction & Uniform
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§ 6.1, 6.2
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Pg. 211-216
6.1, 6.15, 6.32,
6.34, 6.39, 6.41
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Gamma Family
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§ 6.3
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Beta
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§ 6.4
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Normal
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§ 6.5
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Pg. 225-229
6.49, 6.58, 6.63,
6.65, 6.70, 6.72
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Normal Approximations
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§ 6.6
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Bivariate Normal
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§ 6.7
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Pg. 233-234
6.76, 6.82, 6.83
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CHAPTER 7. FUNCTIONS
OF RANDOM VARIABLES
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Introduction & Distribution
Function Techniques
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§ 7.1, 7.2
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Pg. 239-241
7.1, 7.8, 7.12,
7.13
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Transformation Technique
(one variable)
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§ 7.3
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Pg. 256-261
7.16, 7.24, 7.30, 7.38,
7.49
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Transformation Technique
(several variables)
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§ 7.4
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Moment Generating Function
Technique
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§ 7.5
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Pg. 263-265
7.57, 7.61, 7.64,
7.67
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CHAPTER 8. SAMPLING
DISTRIBUTIONS
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Introduction & Sample
Mean
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§ 8.1, 8.2
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Pg. 275-279
8.2, 8.4, 8.5, 8.18,
8.19, 8.24, 8.27, 8.34
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Sample Mean (Finite Populations)
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§ 8.3
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Chi-Square
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§ 8.4
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Pg. 289-293
8.39, 8.40, 8.41, 8.55,
8.61, 8.64, 8.65,
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t
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§ 8.5
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F
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§ 8.6
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Order Statistics
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§ 8.7
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Pg. 296-298
8.75, 8.87
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CHAPTER 9. DECISION
THEORY
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Introduction & Theory
of Games
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§ 9.1, 9.2
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Pg. 308-312
9.4, 9.8, 9.11,
9.13, 9.15, 9.16
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Statistical Games
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§ 9.3
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Pg. 319-321
9.22, 9.24, 9.27
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Decision Criteria
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§ 9.4
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Minimax Criterion
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§ 9.5
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Bayes Criterion
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§ 9.6
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CHAPTER 10. ESTIMATION:
THEORY
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Introduction & Unbiasedness
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§ 10.1, 10.2
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Pg. 330-334
10.1, 10.7, 10.16,
10.23, 10.32, 10.34
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Efficiency
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§ 10.3
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Consistency
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§ 10.4
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Pg. 342-343
10.38, 10.39, 10.45,
10.46, 10.47, 10.51
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Sufficiency
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§ 10.5
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Robustness
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§ 10.6
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Method of Moments
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§ 10.7
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Pg. 349-352
10.55, 10.58, 10.64,
10.66, 10.74, 10.80, 10.87
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Method of Maximum Likelihood
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§ 10.8
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Bayesian Estimation
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§ 10.9
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Pg. 358-359
10.92, 10.97
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CHAPTER 11. ESTIMATION:
APPLICATIONS
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Introduction & Mean
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§ 11.1, 11.2
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Pg. 368-372
11.2, 11.5, 11.11,
11.16, 11.19, 11.26, 11.27
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Difference Between Means
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§ 11.3
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Proportions
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§ 11.4
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Pg. 376-378
11.29, 11.30, 11.35,
11.36, 11.40, 11.44, 11.47, 11.49
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Difference Between Proportions
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§ 11.5
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Variance
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§ 11.6
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Pg. 380-381
11.52, 11.56, 11.59
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Ratio of Two Variances
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§ 11.7
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Use of Computers
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§ 11.8
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CHAPTER 12. HYPOTHESIS
TESTING: THEORY
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Intro. & Statistical
Hypothesis
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§ 12.1, 12.2
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Pg. 392-396
12.1, 12.3, 12.8, 12.12,
12.18, 12.22, 12.24, 12.25
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Losses & Risks
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§ 12.3
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Neyman-Pearson Lemma
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§ 12.4
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Power Function
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§ 12.5
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Pg. 405-409
12.28, 12.32, 12.33,
12.40, 12.43, 12.44
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Likelihood Ratio Test
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§ 12.6
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CHAPTER 13. HYPOTHESIS
TESTING: APPLICATIONS
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Introduction & Means
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§ 13.1, 13.2
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Pg. 421-425
13.2, 13.7, 13.11,
13.14, 13.20, 13.25, 13.29, 13.30
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Difference Between Means
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§ 13.3
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Variance
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§ 13.4
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Pg. 429
13.36, 13.44
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Proportions
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§ 13.5
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Pg. 435-437
13.45, 13.51, 13.54,
13.55, 13.63, 13.69
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Differences Among k Proportions
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§ 13.6
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Contingency Tables
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§ 13.7
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Pg. 443-446
13.75, 13.78, 13.81,
13.82
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Goodness of Fit
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§ 13.8
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Use of Computers
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§ 13.9
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CHAPTER 14. REGRESSION
AND CORRELATION
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TBA
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CHAPTER 15. ANALYSIS
OF VARIANCE
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TBA
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CHAPTER 16. NONPARAMETRIC
TESTS
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TBA
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