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.