We consider their theoretical properties and we investigate various notions of optimality. Statistics is about the mathematical modeling of observable phenomena, using stochastic models, and about analyzing data: estimating parameters of the model and testing hypotheses. Dr. Kempthorne. Descriptive statistics summarizes numerical data using numbers and graphs. Statistical Models. 7 Chapter 1 PROBABILITY REVIEW Basic Combinatorics Number of permutations of ndistinct objects: n! MIT 18.655. The mathe-matics in this chapter is prerequisite for the main part of the book, and it is hoped that the reader already has command of the material; otherwise, Chapter 0 can be viewed as providing “just in time” mathematics. Probability density function f(x) = 1 σ √ 2π exp − (x−µ)2 2σ2 EX = µ VarX = σ2 Notation: X ∼ N(µ,σ2) means that X is normally distributed with mean µ and variance σ2. An Introduction to Basic Statistics and Probability – p. 28/40 2. Statistical Models. A family counselor may use statistics to describe patient behavior and the effectiveness of a treatment program. Chapter 0 grew (and is growing) recursively. Inferential statistics uses sample statistics to estimate population parameters. Not all distinct, such as, for example aaabbc: 6! Spring 2016. í. MIT 18.655 Statistical Models The grades ofstudents in a class can be summarized with averages and line graphs. statistics course at the Master’s level at the university, and the course has also become a compulsory course for the Master’s in eScience. Statistics is a branch of mathematics used to summarize, analyze, and interpret what we observe—to make sense or meaning of our observations. Both educations emphasize a computational and data oriented approach to science – in particular the natural sciences. The aim of the notes is to combine the mathematical and theoretical underpinning In these notes, we study various estimation and testing procedures. A social psychologist may use statistics to summarize peer pressure general mathematical background for probability and statistics. 1.