Author | Pitman, Jim. author |
---|---|
Title | Probability [electronic resource] / by Jim Pitman |
Imprint | New York, NY : Springer New York, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4374-8 |
Descript | XI, 560 p. online resource |
1 Introduction -- 1.1 Equally Likely Outcomes -- 1.2 Interpretations -- 1.3 Distributions -- 1.4 Conditional Probability and Independence -- 1.5 Bayesโ Rule -- 1.6 Sequences of Events -- Summary -- Review Exercises -- 2 Repeated Trials and Sampling -- 2.1 The Binomial Distribution -- 2.2 Normal Approximation: Method -- 2.3 Normal Approximation: Derivation (Optional) -- 2.4 Poisson Approximation -- 2.5 Random Sampling -- Summary -- Review Exercises -- 3 Random Variables -- 3.1 Introduction -- 3.2 Expectation -- 3.3 Standard Deviation and Normal Approximation -- 3.4 Discrete Distributions -- 3.5 The Poisson Distribution -- 3.6 Symmetry (Optional) -- Summary -- Review Exercises -- 4 Continuous Distributions -- 4.1 Probability Densities -- 4.2 Exponential and Gamma Distributions -- 4.3 Hazard Rates (Optional) -- 4.4 Change of Variable -- 4.5 Cumulative Distribution Functions -- 4.6 Order Statistics (Optional) -- Summary -- Review Exercises -- 5 Continuous Joint Distributions -- 5.1 Uniform Distributions -- 5.2 Densities -- 5.3 Independent Normal Variables -- 5.4 Operations (Optional) -- Summary -- Review Exercises -- 6 Dependence -- 6.1 Conditional Distributions: Discrete Case -- 6.2 Conditional Expectation: Discrete Case -- 6.3 Conditioning: Density Case -- 6.4 Covariance and Correlation -- 6.5 Bivariate Normal -- Summary -- Review Exercises -- Distribution Summaries -- Discrete -- Continuous -- Beta -- Binomial -- Exponential -- Gamma -- Geometric and Negative Binomial -- Hypergeometrie -- Normal -- Poisson -- Uniform -- Examinations -- Solutions to Examinations -- Appendices -- 1 Counting -- 2 Sums -- 3 Calculus -- 4 Exponents and Logarithms -- 5 Normal Table -- Brief Solutions to Odd-Numbered Exercises