A First Course in Probability Models and Statistical Inference - Softcover

Inhaltsangabe

1 - Introduction to Probability Models of the Real World.- 1.1 Probability Distributions of Random Variables.- Probability Models.- Random Variables and Their Random Experiments.- 1.2 Parameters to Characterize a Probability Distribution.- The Expected Value or Mean of a Random Variable.- The Variance, Measuring the Accuracy of the Mean.- 1.3 Linear Functions of a Random Variable.- 1.4 The Fundamentals of Probability Theory.- Three Basic Rules of Probability.- Bayes' Theorem.- Random Experiments with Equally Likely Outcomes.- Chebyshev's Theorem.- 1.5 Some Review Exercises.- 2 -Understanding Observed Data.- 2.1 Observed Data from the Real World.- Presenting Data Graphically.- Collecting Data.- Simple Random Samples Drawn from a Probability Distribution.- Populations.- Statistical Questions.- Simple Random Samples Drawn from a Population.- 2.2 Presenting and Summarizing Observed Numeric Data.- Measures of Centrality for Observed Numeric Data.- Measures of Spread for Observed Numeric Data.- 2.3 Grouped Data: Suppressing Irrelevant Detail.- Grouped Distributions of Observed Real World Data.- Histograms: Graphical Display of Grouped Relative Frequency Distributions.- 2.4 Using the Computer.- Describing, Picturing, and Comparing Population and Sample Data.- 3 - Discrete Probability Models.- 3.1 Introduction.- 3.2 The Discrete Uniform Distribution.- 3.3 The Hypergeometric Distribution.- Counting Rules.- What Is the Hypergeometric Model.- Calculating the Probabilities.- The Formulas.- 3.4 Sampling with Replacement from a Dichotomous Population.- What Is the Model?.- The Formulas.- 3.5 The Bernoulli Trial.- 3.6 The Geometric Distribution.- What Is the Model?.- The Formulas.- 3.7 The Binomial Distribution.- The Binomial Experiment.- The Binomial Random Variable Itself.- 3.8 The Poisson Distribution.- 3.9 The Negative Binomial Distribution.- 3.10 Some Review Problems.- 4 - Continuous Probability Models.- 4.1 Continuous Distributions and the Continuous Uniform Distribution.- Continuous Distributions.- The Probability Density function.- The Continuous Uniform Distribution.- 4.2 The Exponential Distribution.- Modeling the Reliability of a System.- The Exponential Distribution.- 4.3 The Normal Distribution.- The Normal Distribution as a Model for Measurement Error.- The Normal Distribution as an Abstract Model.- The Standardizing Transformation.- The Normal Probability Plot.- Continuous Approximations to Integer-Valued Random Variables.- The Normal Approximation to the Binomial.- 4.4 The Chi-Squared Distribution.- 4.5 A Few Review Problems.- 5 - Estimation of Parameters.- 5.1 Parameters and Their Estimators.- Estimators-the Entire Context.- 5.2 Estimating an Unknown Proportion.- The Sampling Distribution for % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaGafmiCaaNbaKaaaaa!3D50! $$ \hat p $$.- Estimating the Value of an Unknown p.- Constructing the Confidence Interval for p.- The Exact (Almost) Endpoints of a Confidence Interval for p.- A Less Conservative Approach to the Standard Error for % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaGafmiCaaNbaKaaaaa!3D50! $$ \hat p $$.- Too Many Approximations: Are They Valid?.- The Appropriate Sample Size for a Given Error Tolerance.- 5.3 Estimating an Unknown Mean.- The Estimator % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGe

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