## Chi Square Distribution

Chi Square Distribution Chi square variate is a square of a normal variate having 1 degree of freedom and  chi square distribution is a special case of Gamma distribution. If X is following normal distribution N(μ, σ) then Z=((X-μ)/σ)2 is a chi-square variate with 1 degree of freedom. The generalized form of chi-square variate is … Read more Chi Square Distribution

## 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 plays very important role in machine learning. Especially, in Decision Tree Learning Chi-Square distribution used. In this post, I will … Read more Gamma Function and Gamma Probability Density Function

## 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 are   146  1

## 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 occurrence of event to its probability. i.e. Expectation of random variable X is denoted by E(X). 1- Expectation of a … Read more Expectation in Statistics

## 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 it does not have any elements and it is denoted by fi. 2-Singelton Set A set is called singleton if … Read more Sets and Relations

## Quadratic Form in Linear Algebra

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 is called real quadratic form. Examples of Quadratic Form 1-x12+x22+ 6 x1 x2 is a quadratic form in variables x1 … Read more Quadratic Form in Linear Algebra

## 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. i.e S: N->R. It is common practice to write a sequence S as Sn Examples of Sequences- Sn = <2n+1> … Read more Test for Convergence of Series

## 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} be ordered bases of U and V. If T is a linear transformation such that T:U->V and it is defined … Read more Matrix Representation of a Linear Transformation

## 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 A. Then determinant |A-λI| will result in an equation of the form. Which is called characteristic equation of matrix A … Read more Caley-Hamilton Theorem

## 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 and plotted the functions using python library. Python Codes to Plot Hyperbolic Functions import numpy as np import matplotlib.pyplot as … Read more Logistic Regression