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• ISBN 13:9780134462103

• Author:Claudia Neuhauser, Marcus Roper  

 Calculus for Biology and Medicine
This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For freshman-level, two-semester or three-semester courses in Calculus for Life Sciences. Shows students how calculus is used to analyze phenomena in nature — while providing flexibility for instructors to teach at their desired level of rigor Calculus for Biology and Medicine motivates life and health science majors to learn calculus through relevant and strategically placed applications to their chosen fields. It presents the calculus in such a way that the level of rigor can be adjusted to meet the specific needs of the audience — from a purely applied course to one that matches the rigor of the standard calculus track.   In the 4th Edition, new co-author Marcus Roper (UCLA) partners with author Claudia Neuhauser to preserve these strengths while adding an unprecedented number of real applications and an infusion of modeling and technology. Also available with MyLab Math MyLab™ Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. For the first time, instructors teaching with Calculus for Biology and Medicine can assign text-specific online homework and other resources to students outside of the classroom. NOTE: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134845048 / 9780134845043  Calculus for Biology and Medicine plus MyLab Math with Pearson eText  – Access Card Package, 4/e Package consists of: 0134070046 / 9780134070049  Calculus for Biology and Medicine 0134782895 / 9780134782898  MyLab Math with Pearson eText – Standalone Access Card – for Calculus for Biology and Medicine, 4/e

Calculus for Biology and Medicine 4th Table of contents:

 ontents
Preface
New to This Edition
Features of the Text
Reflections and Outlook
Chapter Summary
How to Use This Book
MyLab Math Online Course (access code required)
Supplements
Derivatives and Integrals
Basic Differentiation Rules
Basic Integration Formulas
Algebra
Quadratic Formula
Factorial notation
Radicals
Exponents
Binomial Formula
Special Factors
Geometry
Distance Formulas
Equations of Lines and Circles
Areas and Volumes
Trigonometry
Definition of the Six Trigonometric Functions
MyLab Math for Calculus for Biology and Medicine, 4e (access code required)
Exercises with Immediate Feedback
Complete eText
Questions that Deepen Understanding
Chapter 1 Preview and Review
A Brief Overview of Calculus
Section 1.1 Precalculus Skills Diagnostic Test
1.2 Preliminaries
1.2.1 The Real Numbers
Solution
Solution
Solution
1.2.2 Lines in the Plane
Solution
Solution
1.2.3 Equation of the Circle
Solution
1.2.4 Trigonometry
Solution
1.2.5 Exponentials and Logarithms
Solution
Solution
Solution
Solution
1.2.6 Complex Numbers and Quadratic Equations
Solution
Solution
Solution
Solution
Section 1.2 Problems
1.2.1
1.2.2
1.2.3
1.2.4
1.2.5
1.2.6
1.3 Elementary Functions
1.3.1 What Is a Function?
Solution
Solution
Solution
1.3.2 Polynomial Functions
Solution
Solution
1.3.3 Rational Functions
Solution
1.3.4 Power Functions
1.3.5 Exponential Functions
Solution
1.3.6 Inverse Functions
Solution
Geometric Relationship Between f(x) and f−1(x)
1.3.7 Logarithmic Functions
Solution
Solution
Solution
1.3.8 Trigonometric Functions
Solution
Section 1.3 Problems
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.3.6
1.3.7
1.3.8
1.4 Graphing
1.4.1 Graphing and Basic Transformations of Functions
Solution
Solution
1.4.2 The Logarithmic Scale
Solution
1.4.3 Transformations into Linear Functions
Exponential Functions
Solution
Solution
Power Functions
Solution
Solution
Applications
Solution
Solution
Solution
1.4.4 From a Verbal Description to a Graph
Section 1.4 Problems
1.4.1
1.4.2
1.4.3
1.4.4
Chapter 1 Review
Key Terms
Review Problems
Chapter 2 Discrete-Time Models, Sequences, and Difference Equations
2.1 Exponential Growth and Decay
2.1.1 Modeling Population Growth in Discrete Time
Solution
2.1.2 Recurrence Equations
2.1.3 Visualizing Recurrence Equations
Nt+1 Against Nt
Reproductive Rate Against Nt
Section 2.1 Problems
2.1.1
2.1.2
2.1.3
2.2 Sequences
2.2.1 What Are Sequences?
Solution
Solution
Solution
2.2.2 Using Spreadsheets to Calculate a Recursive Sequence
2.2.3 Limits
Solution
Solution
Solution
Solution
Formal Definition of Limits
Solution
Limit Laws
Solution
Solution
2.2.4 Recurrence Equations
Solution
Solution
Solution
2.2.5 Using Σ Notation to Represent Sums of Sequences
Solution
Section 2.2 Problems
2.2.1
2.2.2
2.2.3
Formal Definition of Limits:
Formal Definition of Limits:
2.2.4
2.2.5
2.3 Modeling with Recurrence Equations
2.3.1 Density-Dependent Population Growth
Solution
Solution
2.3.2 Density-Dependent Population Growth: The Beverton-Holt Model
Solution
2.3.3 The Discrete Logistic Equation
2.3.4 Modeling Drug Absorption
Solution
Solution
Section 2.3 Problems
2.3.1
2.3.2
2.3.3
2.3.4
Chapter 2 Review
Key Terms
Review Problems
Chapter 3 Limits and Continuity
3.1 Limits
3.1.1 A Non-Rigorous Discussion of Limits
Solution
Solution
Solution
Solution
Solution
3.1.2 Pitfalls of Finding Limits
Solution
Solution
Solution
Solution
3.1.3 Limit Laws
Solution
Solution
Solution
Solution
Solution
Solution
Section 3.1 Problems
3.1.1 and 3.1.2
3.1.3
3.2 Continuity
3.2.1 What Is Continuity?
Solution
Solution
Solution
Solution
Solution
3.2.2 Combinations of Continuous Functions
Proof
Solution
Solution
Solution
Solution
Solution
Solution
Section 3.2 Problems
3.2.1
3.2.2
3.3 Limits at Infinity
Solution
Solution
Section 3.3 Problems
3.4 Trigonometric Limits and the Sandwich Theorem
3.4.1 Geometric Argument for Trigonometric Limits
Proof that limx→01−cos⁡xx=0
Solution
3.4.2 The Sandwich Theorem
Solution
Solution
Proof that limx→0sin⁡xx=1
Section 3.4 Problems
3.4.1
3.4.2
3.5 Properties of Continuous Functions
3.5.1 The Intermediate-Value Theorem and The Bisection Method
Solution
Solution
3.5.2 Using a Spreadsheet to Implement the Bisection Method
3.5.3 A Final Remark on Continuous Functions
Section 3.5 Problems
3.5.1
3.5.2
3.6 A Formal Definition of Limits
Solution
Solution
Solution
Solution
Solution
Solution
Section 3.6 Problems
Chapter 1 Review
Key Terms
Review Problems
Chapter 4 Differentiation
4.1 Formal Definition of the Derivative
Solution
Section 4.1 Problems
4.2 Properties of the Derivative
4.2.1 Interpreting the Derivative
Velocity.
Population Growth
The Rate of a Chemical Reaction
4.2.2 Differentiability and Continuity
Proof
Solution
Section 4.2 Problems
4.2.1
4.2.2
4.3 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
Section 4.3 Problems
4.4 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
4.4.1 The Product Rule
Proof
Solution
Solution
Solution
Solution
4.4.2 The Quotient Rule
Solution
Solution
Proof
Solution
Solution
Solution
Solution
Solution
Section 4.4 Problems
4.4.1
4.4.2
4.5 The Chain Rule
4.5.1 The Chain Rule
Solution
Solution
Solution
Solution
Solution
Proof of the Quotient Rule
Solution
Solution
Solution
Solution
Solution
Solution
4.5.2 Proof of the Chain Rule
Proof of the Chain Rule
Section 4.5 Problems
4.5.1
4.6 Implicit Functions and Implicit Differentiation
4.6.1 Implicit Differentiation
Solution
Solution
Solution
Proof of the Power Rule for Rational Exponents
4.6.2 Related Rates
Solution
Solution
Solution
Section 4.6 Problems
4.6.1
4.6.2
4.7 Higher Derivatives
Solution
Solution
Solution
Solution
Solution
Section 4.7 Problems
4.7
4.8 Derivatives of Trigonometric Functions
Section 4.8 Problems
4.9 Derivatives of Exponential Functions
Solution
Solution
Solution
Solution
Solution
Solution
Section 4.9 Problems
4.10 Derivatives of Inverse Functions, Logarithmic Functions, and the Inverse Tangent Function
4.10.1 Derivatives of Inverse Functions
Solution
Solution
Solution
Solution
4.10.2 The Derivative of the Logarithmic Function
Solution
Solution
Solution
Solution
Solution
Solution
4.10.3 Logarithmic Differentiation
Solution
Solution
Proof
Section 4.10 Problems
4.10.1
4.10.2
4.10.3
4.11 Linear Approximation and Error Propagation
Solution
Solution
Solution
Solution
Section 4.11 Problems
Chapter 4 Review
Key Terms
Review Problems
Chapter 5 Applications of Differentiation
5.1 Extrema and the Mean-Value Theorem
5.1.1 The Extreme-Value Theorem
Solution
Solution
Solution
5.1.2 Local Extrema
Solution
Solution
Proof
Solution
5.1.3 The Mean-Value Theorem
Solution
Proof of Rolle’s Theorem
Proof of the MVT
Solution
Solution
Proof of Corollary 2
Solution
Section 5.1 Problems
5.1.1
5.1.2
5.1.3
5.2 Monotonicity and Concavity
5.2.1 Monotonicity
Proof
Solution
Solution
5.2.2 Concavity
Proof
Solution
Solution
Section 5.2 Problems
5.2.1 and 5.2.2
5.3 Extrema and Inflection Points
5.3.1 Extrema
Solution
Solution
Solution
5.3.2 Inflection Points
Solution
Section 5.3 Problems
5.3.1
5.3.2
5.4 Optimization
Solution
Solution
Solution
Solution
Solution
Section 5.4 Problems
5.5 L’Hôpital’s Rule
Solution
Solution
Solution
Solution
Solution
Solution
0 ⋅ ∞
Solution
Solution
∞−∞
Solution
Solution
00, 1∞, ∞0
Solution
Solution
Section 5.5 Problems
5.6 Graphing and Asymptotes
Solution
Solution
Solution
Solution
Solution
Section 5.6 Problems
5.7 Recurrence Equations: Stability
5.7.1 Exponential Growth
Cobwebbing
5.7.2 Stability: General Case
Stability
Proof
Solution
Solution
5.7.3 Population Growth Models
Solution
Solution
Section 5.7 Problems
5.8 Numerical Methods: The Newton–Raphson Method
Solution
Solution
Solution
Solution
Section 5.8 Problems
5.9 Modeling Biological Systems Using Differential Equations
5.9.1 Modeling Population Growth
5.9.2 Interpreting the Mathematical Model
Solution
Solution
5.9.3 Passage of Drugs Through the Human Body
Solution
Solution
Section 5.9 problems
5.9.1 and 5.9.2
5.9.3
5.10 Antiderivatives
Section 5.10 problems
Chapter 5 Review
Key Terms
Review Problems
Chapter 6 Integration
6.1 The Definite Integral
6.1.1 The Area Problem
6.1.2 The General Theory of Riemann Integrals
Solution
Solution
Solution
Solution
Geometric Interpretation of Definite Integrals
Solution
Solution
Solution
6.1.3 Properties of the Riemann Integral
Proof of (4)
Proof of (5).
Solution
6.1.4 Order Properties of the Riemann Integral
Solution
Solution
Section 6.1 Problems
6.1.1
6.1.2
6.1.3
6.1.4
6.2 The Fundamental Theorem of Calculus
6.2.1 The Fundamental Theorem of Calculus (Part I)
Solution
Solution
6.2.2 Leibniz’s Rule and a Rigorous Proof of the Fundamental Theorem of Calculus
Leibniz’s Rule
Solution
Solution
Solution
Proof of the Fundamental Theorem of Calculus (Part I) (Optional)
6.2.3 Antiderivatives and Indefinite Integrals
Solution
Solution
Solution
Solution
Solution
Solution
6.2.4 The Fundamental Theorem of Calculus (Part II)
Using the FTC (Part II) to Evaluate Definite Integrals.
Solution
Solution
Solution
Solution
Solution
Finding an Integrand
Solution
Solution
Discontinuous Integrand
Solution
Section 6.2 Problems
6.2.1
6.2.2
6.2.3
6.2.4
6.3 Applications of Integration
6.3.1 Cumulative Change
Solution
Solution
Solution
6.3.2 Average Values
Solution
Solution
Solution
6.3.3 The Mean-Value Theorem
Solution
Solution
Proof of the Mean-Value Theorem for Definite Integrals
6.3.4 Areas
Solution
Solution
Solution
6.3.5 The Volume of a Solid
Solution
Solution
Solution
Solution
6.3.6 Rectification of Curves
Solution
Solution
Solution
Section 6.3 Problems
6.3.1
6.3.2
6.3.3
6.3.4
6.3.5
6.3.6
Chapter 6 Review
Key Terms
Review Problems
Chapter 7 Integration Techniques and Computational Methods
7.1 The Substitution Rule
7.1.1 Indefinite Integrals
Solution
Solution
Solution
Solution
Solution
Solution
Solution
7.1.2 Definite Integrals
First Way
Second Way
Solution
Solution
Solution
Solution
Solution
Section 7.1 Problems
7.1.1
7.1.2
7.2 Integration by Parts and Practicing Integration
7.2.1 Integration by Parts
Solution
Solution
Solution
Solution
Solution
Solution
Solution
7.2.2 Practicing Integration
Solution
Solution
Solution
Section 7.2 Problems
7.2.1
7.2.2
7.3 Rational Functions and Partial Fractions
7.3.1 Proper Rational Functions
Solution
Solution
7.3.2 Partial-Fraction Decomposition
First Method
Second Method
Solution
Solution
Solution
7.3.3 Repeated Linear Factors
Solution
Solution
7.3.4 Irreducible Quadratic Factors
Solution
Solution
Solution
Solution
7.3.5 Summary
Case 1a: Q(x) is a product of two distinct linear factors.
Case 1b: Q(x) is a product of two identical linear factors.
Case 2: (Optional) Q(x) is an irreducible quadratic polynomial.
Section 7.3 Problems
7.3.1
7.3.2
7.3.3
7.3.4
7.3.5
7.4 Improper Integrals
7.4.1 Type 1: Unbounded Intervals
Solution
Solution
Solution
Solution
Solution
7.4.2 Type 2: Unbounded Integrand
Solution
Solution
Solution
7.4.3 A Comparison Result for Improper Integrals
Solution
Solution
Section 7.4 Problems
7.4.1, 7.4.2
7.4.3
7.5 Numerical Integration
7.5.1 The Midpoint Rule
Solution
Solution
7.5.2 The Trapezoidal Rule
Solution
Solution
7.5.3 Using a Spreadsheet for Numerical Integration
Solution
7.5.4 Estimating Error in a Numerical Integration
Section 7.5 Problems
Sections 7.5.1, 7.5.2
7.5.3
7.5.4
7.6 The Taylor Approximation
7.6.1 Taylor Polynomials
Solution
Solution
Solution
Solution
7.6.2 The Taylor Polynomial about x=a
Solution
7.6.3 How Accurate Is the Approximation?
Solution
Solution
Section 7.6 Problems
7.6.1
7.6.2
7.6.3
7.7 Tables of Integrals
Solution
Solution
Solution
Solution
Solution
Solution
Section 7.7 Problems
Chapter 7 Review
Key Terms
Review Problems
Chapter 8 Differential Equations
8.1 Solving Separable Differential Equations
8.1.1 Pure-Time Differential Equations
Solution
8.1.2 Autonomous Differential Equations
Solution
Solution
Solution
Solution
8.1.3 General Separable Equations
Solution
Section 8.1 Problems
8.1.1
8.1.2
8.1.3
8.2 Equilibria and Their Stability
8.2.1 Equilibrium Points
Solution
Solution
8.2.2 Graphical Approach to Finding Equilibria
8.2.3 Stability of Equilibrium Points
Solution
Solution
Solution
Solution
Solution
8.2.4 Sketching Solutions Using the Vector Field Plot
Solution
Solution
8.2.5 Behavior Near an Equilibrium
Solution
Section 8.2 Problems
8.2.1
8.2.2, 8.2.3
8.2.4
8.2.5
8.3 Differential Equation Models
8.3.1 Compartment Models
8.3.2 An Ecological Model
8.3.3 Modeling a Chemical Reaction
8.3.4 The Evolution of Cooperation
8.3.5 Epidemic Model
Section 8.3 Problems
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.4 Integrating Factors and Two-Compartment Models
8.4.1 Integrating Factors
Solution
Solution
Solution
Solution
8.4.2 Two-Compartment Models
Solution
Solution
Section 8.4 Problems
8.4.1
8.4.2
Chapter 8 Review
Key Terms
Review Problems
Chapter 9 Linear Algebra and Analytic Geometry
9.1 Linear Systems
9.1.1 Graphical Solution
Solution
Solution
Solution
9.1.2 Solving Equations Using Elimination
Solution
9.1.3 Solving Systems of Linear Equations
Solution
Solution
Solution
Solution
9.1.4 Representing Systems of Equations Using Matrices
Solution
Solution
Solution
Solution
Section 9.1 Problems
9.1.1, 9.1.2
9.1.3
9.1.4
9.2 Matrices
9.2.1 Matrix Operations
Solution
Solution
Solution
9.2.2 Matrix Multiplication
Solution
Solution
Solution
Solution
Solution
9.2.3 Inverse Matrices
Solution
Solution
Solution
Solution
Solution
Solution
9.2.4 Computing Inverse Matrices
Solution
Solution
Section 9.2 Problems
9.2.1, 9.2.2
9.2.3
9.2.4
9.3 Linear Maps, Eigenvectors, and Eigenvalues
9.3.1 Graphical Representation
Vectors
Solution
Solution
Linear Maps
Solution
9.3.2 Eigenvalues and Eigenvectors
Solution
Solution
Solution
Solution
Solution
Solution
9.3.3 Iterated Maps (Needed for Section 9.4 and 10.9)
Solution
Section 9.3 Problems
9.3.1
9.3.2
9.3.3
9.4 Demographic Modeling
9.4.1 Modeling with Leslie Matrices
Solution
Solution
9.4.2 Stable Age Distributions in Demographic Models
Solution
Solution
Section 9.4 Problems
9.4.1
9.4.2
9.5 Analytic Geometry
9.5.1 Points and Vectors in Higher Dimensions
Vector Representation
Solution
Length of a Vector
Solution
Solution
9.5.2 The Dot Product
Solution
The Angle between Two Vectors
Solution
Solution
Solution
Lines in the Plane
Solution
Planes in R3
Solution
9.5.3 Parametric Equations of Lines
Solution
Solution
Solution
Solution
Section 9.5 Problems
9.5.1
9.5.2
9.5.3
Chapter 9 Review
Key Terms
Review Problems
Chapter 10 Multivariate Calculus
10.1 Functions of Two or More Independent Variables
10.1.1 Defining a Function of Two or More Variables
Solution
Solution
Solution
10.1.2 The Graph of a Function of Two Independent Variables-Surface Plot
10.1.3 Heat Maps
Solution
10.1.4 Contour Plots
Solution
Solution
Section 10.1 Problems
10.1.1
10.1.2
10.1.3
10.1.4
10.2 Limits and Continuity
10.2.1 Informal Definition of Limits
Limits of Polynomials When the Limits Exist.
Limits of Rational Functions When the Limits Exist.
Limits That Do Not Exist.
Solution
Solution
10.2.2 Continuity
Solution
Composition of Functions.
10.2.3 Formal Definition of Limits
Solution
Section 10.2 Problems
10.2.1
10.2.2
10.2.3
10.3 Partial Derivatives
10.3.1 Functions of Two Variables
Solution
Solution
Geometric Interpretation.
Solution
A Biological Application — Prey Capture
10.3.2 Functions of More Than Two Variables
Solution
10.3.3 Higher-Order Partial Derivatives
Solution
Section 10.3 Problems
10.3.1
10.3.2
10.3.3
10.4 Tangent Planes, Differentiability, and Linearization
10.4.1 Functions of Two Variables
Tangent Planes.
Solution
Differentiability.
Solution
Solution
Linearization.
Solution
Solution
10.4.2 Vector-Valued Functions
Solution
Solution
Solution
Solution
Section 10.4 Problems
10.4.1
10.4.2
10.5 The Chain Rule and Implicit Differentiation
10.5.1 The Chain Rule for Functions of Two Variables
Solution
Solution
Solution
10.5.2 Implicit Differentiation
Solution
Solution
Section 10.5 Problems
10.5.1
10.5.2
10.6 Directional Derivatives and Gradient Vectors
10.6.1 Deriving the Directional Derivative
Deriving the Directional Derivative Using the Chain Rule.
Deriving the Directional Derivative Without Using the Chain Rule.
Solution
Solution
10.6.2 Properties of the Gradient Vector
Solution
Solution
Section 10.6 Problems
10.6
10.7 Maximization and Minimization of Functions
10.7.1 Local Maxima and Minima
Solution
Solution
Solution
Solution
A Sufficient Condition Based on Eigenvalues (Optional).
Solution
Solution
Solution
10.7.2 Global Extrema
Solution
Solution
Solution
10.7.3 Extrema with Constraints
Solution
Solution
Solution
Solution
10.7.4 Least-Squares Data Fitting
Solution
Solution
Section 10.7 Problems
10.7.1 and 10.7.2
10.7.3
10.7.4
10.8 Diffusion
Section 10.8 Problems
10.8
10.9 Systems of Recurrence Equations *
10.9.1 A Biological Example
10.9.2 Equilibria and Stability in Systems of Linear Recurrence Equations
Solution
Solution
10.9.3 Equilibria and Stability of Nonlinear Systems of Recurrence Equations
Solution
Solution
Solution
Solution
Section 10.9 Problems
10.9.1
10.9.2
10.9.3
Chapter 10 Review
Key Terms
Review Problems
Chapter 11 Systems of Differential Equations
11.1 Linear Systems: Theory
Solution
11.1.1 The Vector Field
11.1.2 Solving Linear Systems
Specific Solutions.
The General Solution.
Solution
11.1.3 Equilibria and Stability
11.1.4 Systems with Complex Conjugate Eigenvalues
Where Do the Oscillations Come From?
Solution
11.1.5 Summary of the Theory of Linear Systems
Section 11.1 Problems
11.1.1
11.1.2
11.1.3
11.1.4
11.1.5
11.2 Linear Systems: Applications
11.2.1 Two-Compartment Models
Solving the system when c=d=0
Solution
Solution
Solution
11.2.2 A Mathematical Model for Love
11.2.3 The Harmonic Oscillator
Section 11.2 Problems
11.2.1
11.2.2
11.2.3
11.3 Nonlinear Autonomous Systems: Theory
11.3.1 Analytical Approach
A Single Autonomous Differential Equation.
Solution
Systems of Two Differential Equations.
Solution
Solution
11.3.2 Graphical Approach for 2×2 Systems
Solution
Section 11.3 Problems
11.3.1
11.3.2
11.4 Nonlinear Systems: Lotka–Volterra Model for Interspecific Interactions
11.4.1 Competition
Zero Isoclines.
Interpreting the Conditions for Coexistence.
Linearization.
11.4.2 A Predator–Prey Model
Section 11.4 Problems
11.4.1
11.4.2
11.5 More Mathematical Models
11.5.1 The Community Matrix
Mutualism
Competition
Commensalism and Amensalism
Predation
11.5.2 Neuron Activity
11.5.3 Enzymatic Reactions
11.5.4 Microbial Growth in a Chemostat
11.5.5 A Model for Epidemics
Solution
Solution
Section 11.5 Problems
11.5.1
11.5.2
11.5.3
11.5.4
11.5.5
Lethal Diseases
Relapsing Infections
Chapter 11 Review
Key Terms
Review Problems
Chapter 12 Probability and Statistics
12.1 Counting
12.1.1 The Multiplication Principle
Solution
Solution
12.1.2 Permutations
Solution
Solution
Solution
12.1.3 Combinations
Solution
Solution
12.1.4 Combining the Counting Principles
Solution
Solution
Solution
Solution
Solution
Solution
Section 12.1 Problems
12.1.1
12.1.2
12.1.3
12.1.4
12.2 What Is Probability?
12.2.1 Basic Definitions
Basic Set Operations
Solution
The Definition of Probability
Solution
Solution
12.2.2 Equally Likely Outcomes
Solution
Solution
Solution
An Application from Genetics
Solution
The Mark–Recapture Method
Solution
Solution
Solution
Section 12.2 Problems
12.2.1
12.2.2
Color Blindness
12.3 Conditional Probability and Independence
12.3.1 Conditional Probability
Solution
Solution
12.3.2 The Law of Total Probability
Solution
Solution
12.3.3 Independence
Solution
Solution
Solution
Solution
12.3.4 The Bayes Formula
Section 12.3 Problems
12.3.1
12.3.2
12.3.3
12.3.4
12.4 Discrete Random Variables and Discrete Distributions
12.4.1 Discrete Distributions
Solution
Solution
12.4.2 Mean and Variance
The Average Value, or the Mean, of a Discrete Random Variable
Solution
The Variance of a Discrete Random Variable
Solution
Solution
Solution
Solution
Solution
Joint Distributions
Solution
Solution
Solution
Solution
Solution
12.4.3 The Binomial Distribution
Solution
Solution
Down Syndrome
Solution
Solution
Solution
Sampling With and Without Replacement.
Solution
Solution
12.4.4 The Multinomial Distribution
Solution
Solution
12.4.5 Geometric Distribution
Solution
Solution
Solution
Solution
Solution
12.4.6 The Poisson Distribution
Solution
Solution
Solution
Solution
Solution
Section 12.4 Problems
12.4.1
12.4.2
12.4.3
12.4.4
12.4.5
12.4.6
12.5 Continuous Distributions
12.5.1 Density Functions
Solution
Solution
Solution
Seed Dispersal
Solution
12.5.2 The Normal Distribution
Solution
Solution
Solution
Using the Table to Find Probabilities
Solution
Solution
Solution
A Note on Samples
Solution
12.5.3 The Uniform Distribution
Solution
Solution
12.5.4 The Exponential Distribution
Solution
Solution
Radioactive Decay
Solution
Seed Dispersal
Solution
Solution
12.5.5 The Poisson Process
Continuation of Example 14
Solution
12.5.6 Aging
Non-aging
Solution
Aging
Solution
Fruit Fly Lifetimes
Solution
Section12.5 Problems
12.5.1
12.5.2
12.5.3
12.5.4
12.5.5
12.5.6
12.6Limit Theorems
12.6.1 The Law of Large Numbers
proof
proof
Solution
Solution
Solution
12.6.2 The Central Limit Theorem
Solution
Solution
Solution
Solution
Estimating Sample Sizes
Solution
Section12.6 Problems
12.6.1
12.6.2
Cystic Fibrosis
12.7 Statistical Tools
12.7.1 Describing Univariate Data
Solution
Solution
Solution
12.7.2 Estimating Parameters
Point Estimates of Means
Solution
A Remark on Using the Sample Mean to Estimate the Mean
Point Estimates of Proportions
Solution
Solution
Point Estimates of Variances
Solution
Confidence Intervals
Solution
Solution
Solution
Interpreting Mean±S.E.
Solution
12.7.3 Linear Regression
Solution
Solution
Section12.7 Problems
12.7.1
12.7.2
12.7.3
Chapter 1 Review
Key Terms
Review Problems
Appendices

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