Chi Square Distribution

Chi Square Distribution PDF

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

Linear Programming Problem Solution in Python

Linear Programming Problem

Linear Programming Problem The problem of formulating an objective function and constraints an establishing relationship between variables is called a programming problem (LPP). If objective function and constraints are linear then the problem is called linear programming problem. Example- Sometimes, you come across the situation when you need to optimize your algorithm. If you can … Read more Linear Programming Problem Solution in Python

Classification of Second Order Partial Differential Equations

classification of second order partial differential equations

If z is a function of two independent variables x and y. Then second order partial differential equation Rr+Ss+Tt+ f(x,y,z,p,q)=0 Where r, s and t are and R, S and T are continuous functions of x and y in domain of xy-plane. Then if S2-4RT > 0 Then equation is hyperbolic S2-4RT= 0 Then equation … Read more Classification of Second Order Partial Differential Equations

Caley-Hamilton Theorem

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

Logistic Distribution PDF

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

Linear Regression in Statistics

Calculation-for-Regression-Line

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 axis. That best fits the data set, which predicts the value of y for a given x or vice versa. … Read more Linear Regression in Statistics

Poisson Distribution as a Limiting Case of Binomial Distribution

For large value of n binomial distribution asymptotically tends to Poisson distribution. Probability distribution  function of binomial random variable  is Probability distribution of Poisson random variable is Poisson Distribution as a Limiting Case of Binomial Distribution Python Code for Binomial Distribution from scipy.stats import binom import numpy as np import matplotlib.pyplot as plt # Let … Read more Poisson Distribution as a Limiting Case of Binomial Distribution

Exponential Probability Distribution

Mean of Exponentially Distributed Random Variable X

A random variable X is said to follow exponential distribution if it follows the following probability mass function. Exponential probability distribution is a continuous distribution. Probability Distribution Function of Exponentially Distributed Variable X   It is heavily used in the Internet traffic modelling and of study queuing models. Numerical Example- Problem- If a computer receives … Read more Exponential Probability Distribution

Poisson Distribution in Statistics

Mean of Poisson Distribution Variable X

A random variable X is said to follow Poisson distribution, if it follows the following probability distribution function. Poisson distribution is a discrete probability distribution. It models the following types of problems Find out number  of new born babies in a city in certain time duration. Find out defective materials in manufactured by a company. … Read more Poisson Distribution in Statistics

Central Limit Theorem and Normal Distribution

Area Under Normal Distribution Curve

  Why is normal distribution is important? To understand the question you have to go through the Central Limit Theorem. Central Limit Theorem According to central limit theorem if X1, X2, X3,……Xn are random variables drawn from any probability distribution function with mean  Σμi  and standard deviation Σσi where (i=1,2,3,……n). The sum of random variables … Read more Central Limit Theorem and Normal Distribution