A first course in probability and statistics

Includes index.

Probability, 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.

Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background. Suitable for first-year graduate students in statistics, bio-statistics, social sciences and business administration programs, this book provides an exposition of the theory of probability along with applications in statistics