Description
Book SynopsisExplanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level.Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications.
Table of ContentsProbability, Conditional Probability, Independence; Discrete Probability Distributions, Probability Generating Function; Distribution Function, Probability Density Function, Expectation and Variance, Moments, Moment Generating Function, Functions of a Random Variable, Standard Continuous Probability Distributions; Bivariate Probability Distributions, Conditional Distributions, Independence, Expectation of a Function of a Random Vector, Correlation and Regression, Moment Generating Function, Multivariate Probability Distributions; Functions of Two Random Variables, Functions of Multivariate Random Vectors, Sampling Distributions, Chebyshev's Inequality, Weak Law of Large Numbers, Poisson Approximation to a Binomial Distribution, Central Limit Theorem, Normal Approximation to a Binomial Distribution, Approximation to a Chi-Square Distribution by a Normal Distribution, Convergence of Sequences of Random Variables; Methods of Estimation, Cramer-Rao Inequality, Efficient Estimation, Sufficient Statistics, Properties of a Maximum Likelihood Estimator, Bayes Estimation, Estimation of a Probability Density Function; Interval Estimation (Confidence Intervals), Testing of Hypotheses, Chi-Square Tests; Simple Linear Regression Model, Multiple Linear Regression Model, Correlation.
