Schaum's Outline Of Theory and Problems of Probability and Statistics

By: Spiegel, Murray RContributor(s): Schiller, John J | Srinivasan, R.AluMaterial type: TextTextSeries: Schaum's outline seriesPublication details: New Delhi: Tata McGraw-Hill, 2004Edition: 2nd EditionDescription: viii, 408 pages : illustrationsISBN: 9780071350044; 0070586101 Subject(s): Probabilities -- Problems, exercises, etcDDC classification: 519.2
Contents:
Probability -- Random Experiments -- Sample Spaces -- Events -- The Concept of Probability -- The Axioms of Probability -- Some Important Theorems on Probability -- Assignment of Probabilities -- Conditional Probability -- Theorems on Conditional Probability -- Independent Events -- Bayes' Theorem or Rule -- Combinatorial Analysis -- Fundamental Principle of Counting -- Tree Diagrams -- Permutations -- Combinations -- Binomial Coefficients -- Stirling's Approximation to n! -- Random Variables and Probability Distributions -- Random Variables -- Discrete Probability Distributions -- Distribution Functions for Random Variables -- Distribution Functions for Discete Random Variables -- Continuous Random Variables -- Graphical Intepretations -- Joint Distributions -- Independent Random Variables -- Change of Variables -- Probability Distributions of Functions of Random Variables -- Convolutions -- Conditional Distributions -- Applications to Geometric Probability -- Mathematical Expectation -- Definition of Mathematical Expectation -- Functions of Randem Variables -- Some Theorems on Expectation -- The Variance and Standard Deviation -- Some Theorems on Variance -- Standardized Random Variables -- Moments -- Moment Generating Functions -- Some Theorems on Moment Generating Functions -- Characteristics Functions -- Variance for Joint Distributions -- Covariance -- Correlation Coefficient -- Conditional Expectation, Variance, and Moments -- Chebyshev's Inequality -- Law of Large Numbers -- Other Measures of Central Tendency -- Percentiles -- Other Measures of Dispersion -- Skewness and Kurtosis -- Special Probability Distributions -- The Binomial Distribution -- Some Properties of the Binomial Distribution -- The Law of Large Numbers for Bernoulli Trials -- The Normal Distribution -- Some Properties of the Normal Distribution -- Relation Between Binomial and Normal Distributions -- The Poisson Distribution -- Some Properties of the Poisson Distribution -- Relation Between the Binomial and Poisson Distribution -- Relation Between the Poisson and Normal Distributions -- The Central Limit Theorem -- The Multinomial Distribution -- The Hypergeometric Distribution -- The Uniform Distribution -- The Cauchy Distribution -- The Gamma Distribution -- The Beta Distribution -- The Chi-Square Distribution -- Student's t Distribution -- The F Distribution -- Relationships Among Chi-Square, t, and F Distributions -- The Bivariate Normal Distribution -- Miscellaneous Distributions -- Statistics -- Sampling Theory -- Population and Sample -- Statistical Interference -- Sampling With and Without Replacement -- Random Samples -- Random Numbers -- Population Parameters -- Sample Statistics -- Sampling Distributions -- The Sample Mean -- Sampling Distribution of Means -- Sampling Distribution of Proportions -- Sampling Distribution of Differences and Sums -- The Sample Variance -- Sampling Distribution of Variances -- Case where Population Variance Is Unknown -- Sampling Distribution of Ratios of Variances -- Other Statistics -- Frequency Distributions -- Relative Frequency Distributions -- Computation of Mean, Variance, and Moments for Grouped Data -- Estimation Theory -- Unbiased Estimates and Efficient Estimates -- Point Estimates and Interval Estimates -- Reliability -- Confidence Interval Estimates of Population Parameters -- Confidence Intervals for Means -- Confidence Intervals for Proportions -- Confidence Intervals for Differences and Sums -- Confidence Intervals for the Variance of a Normal Distribution -- Confidence Intervals for Variance Ratios -- Maximum Likelihood Estimates -- Tests of Hypotheses and Significance -- Statistical Decisions -- Statistical Hypotheses -- Null Hypotheses -- Tests of Hypotheses and Significance -- Type I and Type II Errors -- Level of Significance -- Tests Involving the Normal Distribution -- One-Tailed and Two-Tailed Tests -- P Value -- Special Tests of Significance for Large Samples -- Special Tests of Significance for Small Samples -- Relationship Between Estimation Theory and Hypothesis Testing -- Operating Characteristic Curves -- Power of a Test -- Quality Control Charts -- Fitting Theoretical Distributions to Sample Frequency Distributions -- The Chi-Square Test for Goodness of Fit -- Contingency Tables -- Yates' Correction for Continuity -- Coefficient of Contingency -- Curve Fitting, Regression, and Correlation -- The Method of Least Squares -- The Least-Squares Line -- The Least-Squares Line in Terms of Sample Variances and Covariance -- The Least-Squares Parabola -- Multiple Regression -- Standard Error of Estimate -- The Linear Correlation Coefficient -- Generalized Correlation Coefficient -- Rank Correlation -- Probability Interpretation of Regression -- Probability Interpretation of Correlation -- Sampling Theory of Regression -- Sampling Theory of Correlation -- Correlation and Dependence -- Analysis of Variance -- The Purpose of Analysis of Variance -- One-Way Classification or One-Factor Experiments -- Total Variation -- Variation Within Treatments -- Variation Between Treatments -- Shortcut Methods for Obtaining Variations -- Linear Mathematical Model for Analysis of Variance -- Expected Values of the Variations -- Distributions of the Variations -- The F Test for the Null Hypothesis of Equal Means -- Analysis of Variance Tables -- Modifications for Unequal Numbers of Observations -- Two-Way Classification or Two-Factor Experiments -- Notation for Two-Factor Experiments -- Variations for Two-Factor Experiments -- Analysis of Variance for Two-Factor Experiments -- Two-Factor Experiments with Replication -- Experimental Design -- Nonparametric Tests -- The Sign Test -- The Mann-Whitney U Test -- The Kruskal-Wallis H Test -- The H Test Corrected for Ties -- The Runs Test for Randomness -- Further Applications of the Runs Test -- Spearman's Rank Correlation.
Summary: Helps to master probability and statistics. This guide includes chapters such as: Basic Probability; Random Variables and Probability Distributions; Mathematical Expectation; Special Probability
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Includes Index

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


Helps to master probability and statistics. This guide includes chapters such as: Basic Probability; Random Variables and Probability Distributions; Mathematical Expectation; Special Probability

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