TY - BOOK AU - Spiegel, Murray R. AU - Schiller, John J. AU - Srinivasan, R.Alu TI - Schaum's Outline Of Theory and Problems of Probability and Statistics T2 - Schaum's outline series SN - 9780071350044 U1 - 519.2 PY - 2004/// CY - New Delhi PB - Tata McGraw-Hill, KW - Probabilities -- Problems, exercises, etc N1 - 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 N2 - Helps to master probability and statistics. This guide includes chapters such as: Basic Probability; Random Variables and Probability Distributions; Mathematical Expectation; Special Probability ER -