Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

🔎 Introduction Cochran’s theorem is a cornerstone in statistical theory. It explains when quadratic forms of normal variables follow...

When Does a Quadratic Form Follow a Chi-Square Distribution?

When Does a Quadratic Form Follow a Chi-Square Distribution?

🔎 Motivation Quadratic forms arise in many statistical methods: Sample variance (measuring spread) Regression & ANOVA (part...

Multinomial Distribution: Theory, Applications, and a Real-World Example

Multinomial Distribution: Theory, Applications, and a Real-World Example

🔎 Introduction The multinomial distribution generalizes the binomial distribution to more than two outcomes. It is widely used in stati...

Solving CSIR - NET Mathematical Sciences: February 2022 PART A [Question ID = 21]: The Case of the Exchanged Students

Solving CSIR - NET Mathematical Sciences: February 2022 PART A [Question ID = 21]: The Case of the Exchanged Students

Hello, math enthusiasts! Today, we have an interesting problem involving two sections of students, their average marks, and the impact of e...

Sensitivity Analysis of Bayesian Methods for Misclassified Multivariate Data

Sensitivity Analysis of Bayesian Methods for Misclassified Multivariate Data

Introduction Misclassification is a common issue in data analysis, especially when dealing with multivariate data. It occurs when the observ...

Understanding Point and Interval Estimation: A Comprehensive Guide with example

Understanding Point and Interval Estimation: A Comprehensive Guide with example

Introduction: Point and interval estimation are fundamental concepts in statistics, providing us with tools to make informed inferences abou...

Population and Sample

Population and Sample

W hen we are working with data, we usually work with samples since it is too difficult, time consuming and expensive to work with population...

Multiple measurement, or observation, as row or column vector

Multiple measurement, or observation, as row or column vector

A multiple measurement or observation may be expressed as \[x=[\begin{matrix} 4 & 2 & 0.6 \\ \end{matrix}]\] referring to the p...

What is Outlier?

What is Outlier?

🔎 Introduction In statistics, an outlier is a data point that lies far away from the rest of the observations. Outliers can distort av...

What is Multivariate Analysis?

What is Multivariate Analysis?

When researchers conduct a survey or experiment there are often many variables of interest. Multivariate analysis is a branch of stat...

First four moments of the Poisson distribution

First four moments of the Poisson distribution

First four moments of Poisson distribution The r th moment about origin is given by \[{{{\mu }'}_{r}}=E({{x}^{r}})=\sum\limits_{x=0}^...

What is singular and Non-singular?

What is singular and Non-singular?

If a matrix A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLx...

What is Simple Random Sampling?

What is Simple Random Sampling?

A sampling method is a procedure for selecting sample elements from a population. Simple random sampling refers to a sampling method that h...

Cumulative Distribution Function

Cumulative Distribution Function

If $(X,Y)$ is a two dimensional random variable (discrete or continuous), then $F(x,y)=p\{X\le x\,andY\le y\}$ is called the cumulative di...

Joint Probability Distribution Function

Joint Probability Distribution Function

If (X,Y) is a two dimensional random continuous variable such that \[P\left\{ x-\frac{dx}{2}\le x\le x+\frac{dx}{2},y-\frac{dy}{2}\le...