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...

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...

Conditional Probability Density Function

Conditional Probability Density Function

Let $X$ and $Y$ be two-dimensional random variables defined simultaneously on a sample space $S$. The joint probability function of $X$...

Chi - square Distribution

Chi - square Distribution

The distribution of the chi-square statistic is called the chi-square distribution. In this lesson, we learn to compute the chi-square ...

Moment-generating function

Moment-generating function

In probability theory and statistics, the  moment-generating function  of a random variable is an alternative specification of its probabili...

List of Continuous distributions

List of Continuous distributions

A Arcsine distribution ARGUS distribution B Balding–Nichols model Bates distribution Benini distribution Benktander Gibrat distribution...

Binomial Distribution Explained: Definition, Theory, and Applications

Binomial Distribution Explained: Definition, Theory, and Applications

🔎 Introduction The binomial distribution is one of the most fundamental discrete probability distributions in statistics. It describe...