Mathematics

Gamma Function and Gamma Probability Density Function

Gamma function and Gamma Probability Distribution Gamma function and Gamma probability density both are very important concepts in mathematics and statistics. Furthermore, understanding Gamma function and Gamma probability density helps to understand chi-square distribution which…

Improper Integrals

Improper Integrals In improper integral, either upper limit or lower limit tends to -∞ or ∞. Furthermore, both integrals may approach to infinity one negative infinity -∞ and other is ∞. Examples of improper integrals…

Expectation in Statistics

Expectation  in statistics Expectation  in statistics is the weighted average of a random variable with its probability. Suppose you toss three coins, then think of event to turn heads up. Random variable associates number of…

Sets and Relations

Sets Set is a collection of well-defined objects. Set’s Representation Basically, there are two ways of a set representation. Types of Set 1-Null Set A set is called null set if it is empty or…

Quadratic Form in Linear Algebra An expression is called quadratic form in the variables x1, x2, x3,………….,xn over field F. Where aij i=1,2,3,….n, j=1,2,3,….m are elements of F. If aij are real then quadratic form…

Test for Convergence of Series

To understand test for  convergence of a series you have to understand sequence and series and related concepts. Sequence A sequence S is a function whose domain is natural numbers and range is real numbers….

Matrix Representation of a Linear Transformation

Matrix Representation of a Linear Transformation Suppose U and V are two vector spaces over the same field F of dimensions m and n. Let A = {α1, α2, α 3,……,α3} and B={β1, β2, β3,…….,βn}…

Caley-Hamilton Theorem

To  understand  Caley-Hamilton theorem you have to know about characteristic polynomial. Characteristic Polynomial If A is a square matrix of of size n * n, and I is identity matrix of the same size as…

Logistic Regression

Hyperbolic Functions These functions are very important in regression, classification and to build neural networks. Moreover, it is important to remember expression hyperbolic functions in the form of exponential functions. I have written the expressions…

Linear Regression in Statistics

Linear regression Linear regression refers to find out degree of relationship between two variables in the form of a linear function y=mx+c using statistical techniques. Where m is gradient and c is intercept on y…