Book:Michael C. Gemignani/Calculus and Statistics

Michael C. Gemignani: Calculus and Statistics

Published $\text {1970}$, Addison-Wesley Publishing Company, Inc.

ISBN 0-486-44993-9

An unabridged republication was issued in 2006 by Dover Publications.

Subject Matter

• Calculus
• Probability Theory
• Statistics

Contents

Chapter 1 The basic Concepts of Function and Probability

1.1 Sets and functions

1.2 The notion of probability

1.3 The basic laws of probability

1.4 More basic facts about probabilities

Chapter 2 Some Specific Probabilities

2.1 Sampling without replacement but with regard to order

2.2 Sampling without replacement or regard to order

2.3 Sampling with replacement and with regard to order

2.4 Bayes' Theorem

Chapter 3 Random Variables. Graphs

3.1 Random variables. Admissible ranges

3.2 Graphs of equalities and inequalities

3.3 Properties of functions and graphs

3.4 Continuity

3.5 Summation notation

3.6 Probability distributions

Chapter 4 The Derivative

4.1 The limit of a function

4.2 The derivative of a function

4.3 Basic rules for finding a derivative

4.4 The Chain Rule. Implicit differentiation

Chapter 5 Applications of the Derivative

5.1 Maxima and minima

5.2 More about maxima and minima. Increasing and decreasing functions

5.3 Some theorems about continuous functions

5.4 Higher derivatives and their applications

5.5 The density function of a continuous distribution. The mode

Chapter 6 Sequences and Series

6.1 Sequences and series

6.2 Tests for convergence of series

6.3 Power series

6.4 Taylor's series. Interval of convergence

Chapter 7 Integration

7.1 The definite integral. Area under a graph

7.2 The fundamental theorem of the calculus

7.3 Some basic integrals. The indefinite integral

7.4 Integration by parts and change of variable

7.5 Improper integrals. Tables of integrals

7.6 Numerical methods of integration

Chapter 8 The Integral and Continuous Variates

8.1 Measures of central tendency

8.2 Variation from the norm

8.3 Probability of extreme values. Moment-generating functions

Chapter 9 Some Basic Discrete Distributions

9.1 The rectangular and hypergeometric distributions

9.2 The binomial distribution

9.3 Distributions involving the number of trials until success

9.4 The Poisson distribution

Chapter 10 Other Important Distributions

10.1 The normal distribution

10.2 Student's $t$-distribution

10.3 More about the $t$-distribution

10.4 $\chi^2$-distribution

10.5 Some other distributions

Chapter 11 Hypothesis Testing

11.1 Statistical inference

11.2 More about critical regions

11.3 Some remarks on the design of experiments

11.4 An example

Chapter 12 Functions of Several Variables

12.1 Multivariate functions

12.2 Partial differentiation

12.3 Multiple integration

Chapter 13 Regression and Correlation

13.1 Linear regression

13.2 Measures of correlation

13.3 The coefficient of correlation

13.4 The significance of $r$ and $r^2$

Appendix

Table 1 Common logarithms

Table 2 Areas under the standard normal curve

Table 3 Critical values of chi square

Table 4 Critical values of $t$

Table 5 Critical values of $F$

Table 6 Exponential functions

Table 7 $z = \dfrac 1 2 \ln \left({\dfrac {1 + r} {1 - r} }\right)$

Table 8 Squares, square roots, and reciprocals from $1$ to $1000$

Answers to the Exercises

General Index

Index of Symbols

Table of Integrals