Probability Statistics and Numerical Methods

Probability Statistics and Numerical Methods

Texts

Required:

• “Introductory Statistics: A Problem-Solving Approach”, Stephen Kokoska, Preliminary Edition, W.H. Freeman and Company.
• EE 216 Class notes: Numerical Methods

Instructor: N. Chowdhury

Prerequisite: MATH 124

Major Topics:

Numerical Methods (Part A): Solutions of equations in one variable, Solutions of systems of linear equations, Solutions of systems of nonlinear equations, Lagrange and Newton’s Interpolations, Numerical differentiation and numerical integration, Numerical solutions of differential equations, Fourier series analyses.

Probability and Statistics (Part B): Tabular and graphical representation of data, Probability, Random variables and discrete probability distributions, Continuous probability distributions, Expectation, Confidence interval, Testing of hypotheses, Method of least squares, Software package(s) for statistical analyses.

Lectures :

 Lectures by topic (Powerpoint slides)

Equations in one variable

Systems of linear equations

Systems of non-linear equations

Examples_solutions of systems of non-linear equations

Interpolation

Numerical differentiation and integration

Periodic functions and Fourier series

Initial value problems

Representation of data

Summary numbers

Basic probability terms

Types of events

Multiplication rules and conditional probability

Probability distribution of discrete random variables

Binomial and continuous distributions

Normal distributions

Sampling

Hypothesis testing

Regression analysis

Class Notes

Selected class notes, Some complex figures and tables

Matrix Inversion by Gauss-Jordan Elimination (Review material)

Matrix Inversion by Determinant and Adjoint (Review material)

Solutions of Systems of Linear Equations

Solutions of Systems of Nonlinear Equations

Numerical Differentiation and Integration

Periodic Functions and Fourier Series

Figure_Histogram

Figure_Cumulative Frequency Diagram

Table_Grouped Frequencies

Figure_Probability of a Continuous Random Variable

Figure: A Probability Density Function

Figure: Probability of  X Between 1 and 2

Figure: Cumulative Probability of X, F(x1)

Normal Distribution

Figure: Probability of X between x1 and x2

Figure: Cumulative Probability of X

Figure: Probability of X greater than

Figure: Probability of X less than

Sampling & Combination of Variables

Hypothesis Testing

An Example on Linear Regression