Weighing the Odds: A Course in Probability and Statistics Book

	Preface
1	Introduction	1
	Conditioning: an intuitive first look	1
	Sharpening our intuition	18
	Probability as Pure Maths	23
	Probability as Applied Maths	25
	First remarks on Statistics	26
	Use of Computers	31
2	Events and Probabilities	35
	Possible outcome [omega], actual outcome [omega] [superscript act.], and Events	36
	Probabilities	39
	Probability and Measure	42
3	Random Variables, Means and Variances	47
	Random Variables	47
	DFs, pmfs and pdfs	50
	Means in the case when [Omega] is finite	56
	Means in general	59
	Variances and Covariances	65
4	Conditioning and Independence	73
	Conditional probabilities	73
	Independence	96
	Laws of large numbers	103
	Random Walks: a first look	116
	A simple 'strong Markov principle'	127
	Simulation of IID sequences	130
5	Generating Functions; and the Central Limit Theorem	141
	General comments on the use of Generating Functions (GFs)	142
	Probability generating functions (pgfs)	143
	Moment Generating Functions (MGFs)	146
	The Central Limit Theorem (CLT)	156
	Characteristic Functions (CFs)	166
6	Confidence Intervals for one-parameter models	169
	Some commonsense Frequentist CIs	173
	Likelihood; sufficiency; exponential family	181
	Brief notes on Point Estimation	187
	Maximum-Likelihood Estimators (MLEs) and associated CIs	192
	Bayesian Confidence Intervals	199
	Hypothesis Testing - if you must	222
7	Conditional pdfs and multi-parameter Bayesian Statistics	240
	Joint and conditional pmfs	240
	Jacobians	243
	Joint pdfs; transformations	246
	Conditional pdfs	258
	Multi-parameter Bayesian Statistics	265
8	Linear Models, ANOVA, etc	283
	Overview and motivation	283
	The Orthonormality Principle and the F-test	295
	Five basic models: the Mathematics	304
	Goodness of fit; robustness; hierarchical models	339
	Multivariate Normal (MVN) Distributions	365
9	Some further Probability	383
	Conditional Expectation	385
	Martingales	406
	Poisson Processes (PPs)	426
10	Quantum Probability and Quantum Computing	440
	Quantum Computing: a first look	441
	Foundations of Quantum Probability	448
	Quantum computing: a closer look	463
	Spin and Entanglement	472
	Spin and the Dirac equation	485
	Epilogue	491
App. A	Some Prerequisites and Addenda	495
App. B	Discussion of some Selected Exercises	502
App. C	Tables	514
App. D	A small Sample of the Literature	519
	Bibliography	525
	Index	539