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

Gamma Function and Gamma Probability Density Function

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

Expectation in Statistics

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

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

Binomial Distribution in Statistics

Expectation of X in Binomial Distribution

Let X be a random variable, it is said to follow binomial distribution if it follows the following probability mass function. And it can have only non-negative values. The binomial distribution is a discrete probability distribution. Binomial distribution is used to model problems, for instance,  getting  number of success after certain  number of random experiments … Read more Binomial Distribution in Statistics

Uniform Distribution

Uniform-Distributionsize5000.png

Uniform Distribution or Rectangular Distribution Uniform distribution or rectangular distribution is a continuous probability distribution. Definition- A random variable X is said to follow uniform or rectangular distribution it follows the following probability distribution function. And is denoted by X~U(a,b) Python Code to Plot Uniform Distribution import numpy import matplotlib.pyplot as plt a=20 b=50 x= … Read more Uniform Distribution

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