Probability Distributions used in Data Science
In this article we listed 5 probability distributions used in Data Science like Uniform, Bernoulli, Binomial, Poisson, and Normal which are .
Introduction:
Probability is defined as the likeliness of something to occur or happen and probability distributions are functions that give the relation between all the outcomes of a random variable in any random experiment and its probable values.
These distribution functions are used in predicting the stock prices, weather prediction.
In this article, we have listed the 5 most used Probability Distributions in Data Science.
Table of Contents
What is Random Variable?
Set of all possible values from a Random Experiment is called Random Variable.
It is represented by X.
Example: Outcome of coin toss
Types of Random Variable:

Discrete Random Variable


 X is a discrete because it has a countable values between two numbers
 Example : number of balls in a bag, number of tails in tossing coin


Continuous Random Variable

 X is a continuous because it has a infinite number of values between two values
 Example : distance travelled, Height of students
What is Probability Distribution?
A Probability Distribution of a random variable is a list of all possible outcomes with corresponding probability values.
Note : The value of the probability always lies between 0 to 1.
What is an example of Probability Distribution?
Let’s understand the probability distribution by an example:
When two dice are rolled with six sided dots, let the possible outcome of rolling is denoted by (a, b), where
a : number on the top of first dice
b : number on the top of second dice
Then, sum of a + b are:
Sum of a + b  (a, b) 
2  (1,1) 
3  (1,2), (2,1) 
4  (1,3), (2,2), (3,1) 
5  (1,4), (2,3), (3,2), (4,1) 
6  (1,5), (2,4), (3,3), (4,2), (5,1) 
7  (1,6), (2,5), (3,4),(4,3), (5,2), (6,1) 
8  (2,6), (3,5), (4,4), (5,3), (6,2) 
9  (3,6), (4,5), (5,4), (6,3) 
10  (4,6), (5,5), (6,4) 
11  (5,6), (6,5) 
12  (6,6) 
 If a random variable is a discrete variable, it’s probability distribution is called discrete probability distribution.
 Example : Flipping of two coins
 Functions that represents a discrete probability distribution is known as Probability Mass Function.
 If a random variable is a continuous variable, it’s probability distribution is called continuous probability distribution.
 Example: Measuring temperature over a period of time
 Functions that represents a continuous probability distribution is known as Probability Density Function.
Types of Probability Distributions
Uniform Distribution
What is Uniform Distribution?
Probability distribution in which all the outcome have equal probability is known as Uniform Distribution.
Example: Perfect Random Generator
What is an example of Uniform Distribution?
Let’s understand by an example
Consider an experiment of tossing a single coin:
 Random variable X is uniformly distributed if the distribution function is given by:
Bernoulli Distribution
What is Bernoulli Distribution?
A discrete probability distribution for a random experiment that has only two possible outcomes (Bernoulli trials) is known Bernoulli Distribution.
Example: India will win cricket world cup or not
 It has only two possible outcome
 Success (1)
 Failure (0)
 Random variable n is Bernoulli distributed if the distribution function is given by:
What is an example of Bernoulli Distribution?
Let’s understand by an example
Consider an experiment of Shooting of Basketball
Binomial Distribution
What is Binomial Distribution?
A discrete probability distribution that gives only two possible outcomes in n independent trails is known as Binomial Distribution.
Example: Yes/No survey
 Extension of Bernoulli Distribution
 Represent the number of success and failure into n independent trials
 The probability of success and failure is the same for all independent and identical trails.
 Random variable X is binomial distributed if the distribution function is given by:
 Mean = np
 Variance = npq
 Mean > Variance
What is an example of Binomial Distribution?
Let’s understand the Binomial Distribution by an example,
Consider the experiment of Picking Balls
Problem Statement:
Let there are 8 white balls and 2 black balls, then the probability of drawing 3 white balls, if the probability of selecting white ball is 0.6.
Difference between Binomial and Bernoulli’s Distribution
Bernoulli  Binomial 
Deals with the single trial event  Deals with the outcome of Multiple trials of the single events 
Has only two possible outcome 0 and 1  Sum of identically and independent distributed Bernoulli Random Variable 
Poisson Distribution
What is Poisson Distribution?
A discrete probability distribution that measures the probability of a random variable over a specific period of time is known as Poisson Distribution.
Example: Probability of Asteroid collision over a selected year of period.
 Used to predict probability of number of successful events.
 Random variable X is Poisson distributed if the distribution function is given by:
Note: In case of Poisson Distribution Mean = Variance
What is an example of Poisson Distribution?
Let’s understand the Poisson Distribution by an example,
Consider the experiment of Number of patient visiting in a hospital
Problem Statement :
Let in a hospital patient arriving in a hospital at expected value is 6, then what is the probability of five patients will visit the hospital in that day?
Difference between Poisson Distribution and Binomial Distribution
Poisson  Binomial 
Number of trials are infinite  Number of trials are fixed 
Unlimited number of possible outcomes  Only two possible outcomes (Success or Failure) 
Mean = Variance  Mean > Variance 
Normal Distribution (Gaussian Distribution):
A continuous probability distribution, which is symmetric about it’s mean value (i.e. data near the mean are more frequency in occurrence) is known as Normal Distribution.
What is an example of Normal Distribution?
Lets’ understand the Normal Distribution by an example,
Consider the experiment of Number of books read by students in a school
 Random variable X is normally distributed if the distribution function is given by:
Empirical Rule:
Empirical Rule is often called the 68 – 95 – 99.7 rule or Three Sigma Rule. It states that on a Normal Distribution:
 68% of the data will be within one Standard Deviation of the Mean
 95% of the data will be within two Standard Deviations of the Mean
 99.7 of the data will be within three Standard Deviations of the Mean
 Characteristics of Normal Distribution :
 Symmetrical around its mean value
 Mean = Median = Mode
 Total area under the curve is 1
 Curve of the distribution is bell curve
Standard normal distribution
 Normal distribution with mean = 0 and standard deviation = 1.
 For any random Variable X, probability distribution function is given by:
Difference between Poisson and Normal Distribution
Poisson  Normal 
Use Discrete Data  Use Continuous Data 
Distribution vary on mean value  Symmetric about mean value 
Mean = Variance  Mean = Median = Mode 
Probability distributions are not a Graph.
A graph is just a visual representation
Conclusion:
From the article, you will have a clear understanding of Probability Distributions in Data Science. This article highlights 5 important probability distributions with their applications. I hope this article will help you in your Data Science journey.
Frequently Ask Question
Q1. What are the different types of Random Variables?
A1.
Discrete Random Variable X is a discrete because it has a countable values between two numbers
Example : number of balls in a bag, number of tails in tossing coin
Continuous Random Variable X is a continuous because it has a infinite number of values between two values
Example : distance travelled, Height of students
Q2. What is Probability Distribution?
A2. A Probability Distribution of a random variable is a list of all possible outcomes with corresponding probability values.
Note : The value of the probability always lies between 0 to 1.
Q3. Types of Probability Distribution used in Data Science
A3. 1. Uniform Distribution 2. Bernoulli Distribution 3. Binomial Distribution 4. Poisson Distribution 5. Normal Distribution
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FAQs
Types of Random Variables
Discrete Random Variable X is a discrete because it has a countable values between two numbers Example : number of balls in a bag, number of tails in tossing coin Continuous Random Variable X is a continuous because it has a infinite number of values between two values Example : distance travelled, Height of students
What is Probability Distribution?
A Probability Distribution of a random variable is a list of all possible outcomes with corresponding probability values. Note : The value of the probability always lies between 0 to 1.
Types of Probability Distribution
1. Uniform Distribution 2. Bernoulli Distribution 3. Binomial Distribution 4. Poisson Distribution 5. Normal Distribution
Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio