# Book:Michael C. Gemignani/Calculus and Statistics

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## 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.

### 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