# Probability Distributions

## Poisson Distribution Explained

Poisson Distribution outputs the probability of a sequence of events happening in a fixed time interval.

## Uniform Probability Distribution

In a Uniform Distribution Probability Density Function (PDF) is same for all the possible X values. Sometimes this is called a Rectangular Distribution. There are two (2) parameters in this distribution, a minimum (A) and a maximum (B)

## Normal Distribution, Z Scores and Standardization Explained

Normal Distribution is the most important probability distribution in Probability and Statistics. A normal probability distribution is a bell shaped curve. Many numerical populations have distributions that can be fit very closely by an appropriate normal curve.

## Probability Density Function

Earlier we used Probability Mass Function to describe how the total probability of 1 is distributed among the possible values of the Discrete Random Variable X.

## Random Variables in Statistics

A Random Variable is any rule that maps (links) a number with each outcome in sample space S. Mathematically, random variable is a function with Sample Space as the domain. It’s range is the set of Real Numbers.

## Negative Binomial Distribution

In the Negative Binomial Distribution, we are interested in the number of Failures in n number of trials. This is why the prefix “Negative” is there. When we are interested only in finding number of trials that is required for a single success, we called it a Geometric Distribution.

## Binomial Probability Distribution

Binomial Distribution is used to find probabilities related to Dichotomous Population. It can be applied to a Binomial Experiment where it can result in only two outcomes. Success or Failure. In Binomial Experiments, we are interested in the number of Successes.

## Probability Mass Function

Probability Mass Function (PMF) of X says how the total probability of 1 is distributed (allocated to) among the various possible X values.

## Expected Value of a Random Variable

Expected Value is the average value we get for a certain Random Variable when we repeat an experiment a large number of times. It is the theoretical mean of a Random Variable. Expected Value is based on population data. Therefore it is a parameter.