Probability with Statistical Applications Book

	Preface
1	Probability Space	1
1.1	The Axioms of Probability	1
1.2	Conditional Probabilities and Bayes' Formula	6
1.3	Independent Events	13
1.4	Three or More Events	16
2	Random Variables	23
2.1	Discrete Random Variables	23
2.2	Continuous Random Variables	28
2.3	Expectation	32
2.4	Variance	43
2.5	Normal Random Variables	51
3	Binomial and Poisson Random Variables	59
3.1	Counting Principles	59
3.2	Binomial Random Variables	66
3.3	Poisson Random Variables	76
4	Limit Theorems	87
4.1	The Law of Large Numbers	87
4.2	Central Limit Theorem	94
5	Estimation and Hypothesis Testing	103
5.1	Large Sample Estimation	103
5.2	Hypothesis Testing	114
5.3	Small Samples	124
5.4	Chi-Square Tests	133
6	Linear Regression	143
6.1	Fitting a Line to Data	143
6.2	Inference for Regression	152
7	Moment Generating Functions and Sums of Independent Random Variables	161
7.1	Moment Generating Functions	161
7.2	Sums of Independent Random Variables	166
8	Transformations of Random Variables and Random Vectors	177
8.1	Distribution Functions and Transformations of Random Variables	177
8.2	Random Vectors	188
8.3	Chi-square, Student Distributions and Normal Vectors	200
	Appendices	213
	Index	217