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Introduction The Problem of Decision under Uncertainty 1

1．The Meaning of Probability 2

2．Expected Value and Utility 24

3．Random Variables and Probability Distributions 50

Part One The Use of Probabilities Based Directly on Experience 65

4．The Simplest Problems of Inventory Control; Incremental Analysis 66

5．Measures of Location: Fractiles and Expectations; Linear Profits and Costs 79

6．Assessment of Probabilities by Smoothing Historical Frequencies 95

7．Opportunity Loss and the Cost of Uncertainty 117

8．Lump-sum Losses; Scrap Allowances 133

Part Two Simple Random Processes and Derived Probabilities 159

9．Conditional and Joint Probability 160

10．The Bernoulli Process: The Binomial Distribution 174

11．The Bernoulli Process: The Pascal Distribution 183

12．Conditional Models and Marginal Probability 194

13．The Poisson Process: The Poisson Distribution 209

14．The Poisson Process: The Gamma Distribution 221

15．Min-Max Inventory Control 236

16．Measures of Dispersion: The Variance and the Standard Deviation 260

17．The Normal Approximation to Distributions of Sums of Random Variables 274

18．The Normal Approximation to Empirical Distributions 294

19．Waiting Lines 306

20．The Monte Carlo Method 320

Part Three The Use of Information Obtained by Sampling 329

21．Revision of Probabilities in the Light of New Information 330

22．Two-action Problems with Linear Costs 342

23．Samples from Finite Populations: The Hypergeometric Distribution 355

24．Interdependent Decision Problems; Finite vs．Infinite Populations 371

25．Samples from Many-valued Populations; Sufficient Statistics 384

26．Samples from “Normal” Populations with Known Variance 397

27．Samples from “Normal” Populations with Known Mean 405

28．Nuisance Parameters:“Normal” Populations with Both ParametersUnknown 413

29．Populations of Incompletely Specified Form; “Large-sample Theory” 423

30．Normal Prior Distributions 435

31．Biased Measurement and Biased Selection 458

32．Comparison of Two Unknown Quantities; the Importance of Sample Design 486

Part Four The Value of Additional Information 507

33．Evaluation of a Decision to Sample and Then Act; Preposterior Analysis 508

34．Two-action Problems with Linear Costs: Expected Loss and the Prior Dis-tribution of the Posterior Mean 519

35．Two-action Problems with Linear Costs: Optimal Sample Size 536

36．Interdependent Two-action Problems under a Stationary Distribution 553

37．Many-action Problems with Proportional Losses; General-purpose Estima-tion 574

38．Sequential Decision Procedures 590

Part Five Objectivist Statistics: Tests of Significance and Confidence Intervals 605

39．The Classical Theory of Testing Hypotheses 606

40．Evaluation of Statistical Decision Rules in Terms of Expected Loss 624

41．Tests of Significance as Sequential Decision Procedures 644

42．Confidence Intervals 661

Appendix 669

Continuous Prior Distributions for the Parameters of Bernoulli and Poisson Processes 670

Tables 679

Ⅰ．Cumulative Binomial Distribution 680

Ⅱ．Unit Normal Probability Distribution 702

Ⅲ．Cumulative Unit Normal Distribution 704

Ⅳ．Unit Normal Loss Integral 706

Ⅴ．Random Digits 708

Ⅵ．Square Roots 709

Ⅶ．Cube Roots 710

Charts 711

Ⅰ．Cumulative Poisson and Gamma Distributions 711

Ⅱ．Optimal Sample Size: Two-action Problems with Linear Costs 712

Ⅲ．Gamma Probability Distribution 713

Ⅳ．Unit Normal Distribution: Ratio of Ordinate to Left Tail 715

Ⅴ．x/？f Probability Distribution 716

Ⅵ．Optimal Sample Size: Many-action Problems with Proportional Losses 718

Index of Symbols 719

Subject Index 723