# Book:Michael C. Gemignani/Calculus and Statistics

## Michael C. Gemignani: *Calculus and Statistics*

Published $1970$, **Addison-Wesley Publishing Company, Inc.**

- ISBN 0-486-44993-9.

An unabridged republication was issued in 2006 by Dover Publications.

### Subject Matter

### 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**