Frieden B.R. Probability, Statistical Optics, and Data Testing. A Problem Solving Approach

Springer, 2001. — 508 p.Scientists and engineers in optics are increasingly confronted with problems that are of a random nature and that require a working knowledge of probability and statistics for their solution. This book develops these subjects within the context of optics, using a problem-solving approach. All methods are explicitly derived and can be traced back to three simple axioms given at the outset. This third edition contains many new applications to optical and physical phenomena, including a method of exactly estimating probability laws.The Axiomatic Approach
Continuous Random Variables
Fourier Methods in Probability
Functions of Random Variables
Bernoulli Trials and Limiting Cases
The Monte Carlo Calculation
Stochastic Processes
Introduction to Statistical Methods: Estimating the Mean, Median, Variance, SIN, and Simple Probability
Introduction to Estimating Probability Laws
The Chi-Square Test of Significance
The Student t-Test on the Mean
The F-Test on Variance
Least-Squares Curve Fitting - Regression Analysis
Principal Components Analysis
The Controversy Between Bayesians and Classicists
Introduction to Estimation Methods