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| Probability | |
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| Basic Probability | |
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| Random Experiments | |
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| Sample Spaces | |
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| Events | |
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| The Concept of Probability | |
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| The Axioms of Probability | |
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| Some Important Theorems on Probability | |
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| Assignment of Probabilities Conditional Probability | |
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| Theorems on Conditional Probability | |
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| Independent Events Bayes' Theorem or Rule | |
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| Combinatorial Analysis | |
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| Fundamental Principle of Counting Tree Diagrams | |
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| Permutations | |
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| Combinations-' Binomial Coefficients | |
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| Stirling's Approximation to n! | |
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| Random Variables and Probability Distributions | |
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| Random Variables | |
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| Discrete Probability Distributions | |
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| Distribution Functions for Random Variables | |
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| Distribution Functions for Discrete Random Variables | |
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| Continuous Random Variables | |
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| Graphical Interpretations | |
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| Joint Distributions | |
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| Independent Random Variables Change of Variables | |
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| Probability Distributions of Functions of Random Variables | |
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| Convolutions | |
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| Conditional Distributions | |
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| Applications to Geometric Probability | |
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| Mathematical Expectation | |
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| Definition of Mathematical Expectation | |
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| Functions of Random Variables | |
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| Some Theorems on Expectation | |
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| The Variance and Standard Deviation | |
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| Some Theorems on Variance | |
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| Standardized Random Variables | |
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| Moments | |
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| Moment Generating Functions | |
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| Some Theorems on Moment Generating Functions | |
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| Characteristic Functions | |
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| Variance for Joint Distributions. Covariance | |
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| Correlation Coefficient | |
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| Conditional Expectation, Variance, and Moments Chebyshev's Inequality | |
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| Law of Large Numbers | |
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| Other Measures of Central Tendency Percentiles | |
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| Other Measures of Dispersion | |
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| Skewness and Kurtosis | |
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| Special Probability Distributions | |
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| The Binomial Distribution | |
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| Some Properties of the Binomial Distribution | |
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| The Law of Large Numbers for Bernoulli Trials | |
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| The Normal Distribution | |
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| Some Properties of the Normal Distribution | |
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| Relation Between Binomial and Normal Distributions | |
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| The Poisson Distribution | |
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| Some Properties of the Poisson Distribution | |
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| Relation Between the Binomial and Poisson Distributions | |
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| Relation Between the Poisson and Normal Distributions | |
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| The Central Limit Theorem | |
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| The Multinomial Distribution | |
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| The Hypergeometric Distribution | |
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| The Uniform Distribution | |
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| The Cauchy Distribution | |
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| The Gamma Distribution | |
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| The Beta Distribution | |
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| The Chi-Square Distribution | |
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| Student's t Distribution | |
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| The F Distribution | |
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| Relationships Among Chi-Square, t, and F Distributions | |
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| The Bivariate Normal Distribution Miscellaneous Distributions | |
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| Statistics | |
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| Sampling Theory | |
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| Population and Sample. Statistical Inference | |
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| Sampling With and Without Replacement Random Samples. Random Numbers | |
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| Population Parameters | |
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| Sample Statistics Sampling Distributions | |
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| The Sample Mean | |
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| Sampling Distribution of Means | |
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| Sampling Distribution of Proportions | |
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| Sampling Distribution of Differences and Sums | |
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| The Sample Variance | |
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| Sampling Distribution of Variances | |
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| Case Where Population Variance Is Unknown | |
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| Sampling Distribution of Ratios of Variances | |
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| Other Statistics | |
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| Frequency Distributions | |
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| Relative Frequency Distributions | |
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| Computation of Mean, Variance, and Moments for Grouped Data | |
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| Estimation Theory | |
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| Unbiased Estimates and Efficient Estimates | |
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| Point Estimates and Interval Estimates. Reliability | |
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| Confidence Interval Estimates of Population Parameters | |
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| Confidence Intervals for Means | |
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| Confidence Intervals for Proportions Confidence Intervals for Differences and Sums | |
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| Confidence Intervals for the Variance of a Normal Distribution | |
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| Confidence Intervals for Variance Ratios | |
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| Maximum Likelihood Estimates | |
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| Tests of Hypotheses and Significance | |
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| Statistical Decisions | |
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| Statistical Hypotheses. Null Hypotheses | |
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| Tests of Hypotheses and Significance | |
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| Type I and Type II Errors | |
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| Level of Significance | |
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| Tests Involving the Normal Distribution | |
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| One-Tailed and Two-Tailed Tests | |
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| P Value | |
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| Special Tests of Significance for Large Samples | |
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| Special Tests of Significance for Small Samples | |
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| Relationship Between Estimation Theory and Hypothesis Testing | |
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| Operating Characteristic Curves. Power of a Test Quality Control Charts | |
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| Fitting Theoretical Distributions to Sample Frequency Distributions The Chi-Square Test for Goodness of Fit | |
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| Contingency Tables | |
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| Yates' Correction for Continuity | |
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| Coefficient of Contingency | |
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| Curve Fitting, Regression, and Correlation | |
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| Curve Fitting | |
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| Regression | |
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| The Method of Least Squares | |
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| The Least-Squares Line | |
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| The Least-Squares Line in Terms of Sample Variances and Covariance | |
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| The Least-Squares Parabola | |
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| Multiple Regression | |
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| Standard Error of Estimate | |
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| The Linear Correlation Coefficient | |
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| Generalized Correlation Coefficient | |
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| Rank Correlation | |
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| Probability Interpretation of Regression | |
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| Probability Interpretation of Correlation | |
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| Sampling Theory of Regression Sampling Theory of Correlation | |
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| Correlation and Dependence | |
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| Analysis of Variance | |
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| The Purpose of Analysis of Variance | |
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| One-Way Classification or One-Factor Experiments Total Variation. Variation Within Treatments. Variation Between Treatments Shortcut Methods for Obtaining Variations | |
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| Linear Mathematical Model for Analysis of Variance | |
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| Expected Values of the Variations | |
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| Distributions of the Variations | |
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| The F Test for the Null Hypothesis of Equal Means | |
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| Analysis of Variance Tables Modifications for Unequal Numbers of Observations Two-Way Classification or Two-Factor Experiments | |
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| Notation for Two-Factor Experiments | |
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| Variations for Two-Factor Experiments | |
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| Analysis of Variance for Two-Factor Experiments | |
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| Two-Factor Experiments with Replication | |
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| Experimental Design | |
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| Nonparametric Tests | |
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| Introduction | |
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| The Sign Test | |
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| The Mann-Whitney U Test | |
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| The Kruskal-Wallis H Test | |
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| The H Test Corrected for Ties | |
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| The Runs Test for Randomness | |
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| Further Applications of the Runs Test | |
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| Spearman's Rank Correlation | |
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| Bayesian Methods | |
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| Subjective Probability | |
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| Prior and Posterior Distributions | |
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| Sampling From a Binomial Population | |
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| Sampling From a Poisson Population | |
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| Sampling From a Normal Population with Known Variance | |
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| Improper Prior Distributions | |
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| Conjugate Prior Distributions | |
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| Bayesian Point Estimation | |
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| Bayesian Interval Estimation | |
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| Bayesian Hypothesis Tests | |
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| Bayes Factors | |
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| Bayesian Predictive Distributions | |
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| Mathematical Topics | |
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| Special Sums | |
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| Euler's Formulas | |
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| The Gamma Function | |
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| The Beta Function | |
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| Special Integrals | |
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| Ordinates y of the Standard Normal Curve at z | |
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| Areas under the Standard Normal Curve from 0 to z | |
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| Percentile Values t<sub>p</sub> for Student's t Distribution with v Degrees of Freedom | |
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| Percentile Values x<sub>p</sub></sup>2</sup> for the Chi-Square Distribution with v Degrees of Freedom | |
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| 95th and 99th Percentile Values for the F Distribution with v<sub>1</sub> v<sub>2</sub> Degrees of Freedom | |
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| Values of e<sup>-�</sup> | |
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| Random Numbers | |
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| Subject Index | |
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| Index for Solved Problems | |