Tutorial Playlist

Data Structure Tutorial

Overview

Arrays in Data Structures: A Guide With Examples

Lesson - 1

All You Need to Know About Two-Dimensional Arrays

Lesson - 2

All You Need to Know About a Linked List in a Data Structure

Lesson - 3

The Complete Guide to Implement a Singly Linked List

Lesson - 4

The Ultimate Guide to Implement a Doubly Linked List

Lesson - 5

The Fundamentals for Understanding Circular Linked List

Lesson - 6

The Ultimate Guide To Understand The Differences Between Stack And Queue

Lesson - 7

Implementing Stacks in Data Structures

Lesson - 8

Your One-Stop Solution for Stack Implementation Using Array

Lesson - 9

Your One-Stop Solution for Queue Implementation Using Array

Lesson - 10

Your One-Stop Solution to Learn Depth-First Search(DFS) Algorithm From Scratch

Lesson - 11

Your One-Stop Solution for Stack Implementation Using Linked-List

Lesson - 12

The Definitive Guide to Understand Stack vs Heap Memory Allocation

Lesson - 13

All You Need to Know About Linear Search Algorithm

Lesson - 14

All You Need to Know About Breadth-First Search Algorithm

Lesson - 15

A One-Stop Solution for Using Binary Search Trees in Data Structure

Lesson - 16

The Best Tutorial to Understand Trees in Data Structure

Lesson - 17

A Complete Guide to Implement Binary Tree in Data Structure

Lesson - 18

A Holistic Look at Using AVL Trees in Data Structures

Lesson - 19

All You Need to Know About Tree Traversal in Data Structure

Lesson - 20

The Best Guide You’ll Ever Need to Understand B-Tree in Data Structure

Lesson - 21

The Best Guide You'll Ever Need to Understand Spanning Tree in Data Structure

Lesson - 22

The Best and Easiest Way to Understand an Algorithm

Lesson - 23

Your One-Stop Solution to Understand Shell Sort Algorithm

Lesson - 24

Your One-Stop Solution to Quick Sort Algorithm

Lesson - 25

The Most Useful Guide to Learn Selection Sort Algorithm

Lesson - 26

Everything You Need to Know About Radix Sort Algorithm

Lesson - 27

Everything You Need to Know About the Counting Sort Algorithm

Lesson - 28

Everything You Need to Know About the Merge Sort Algorithm

Lesson - 29

Insertion Sort Algorithm: One-Stop Solution That Will Help You Understand Insertion Sort

Lesson - 30

Everything You Need to Know About the Bubble Sort Algorithm

Lesson - 31

The Best Guide You’ll Ever Need to Understand Bucket Sort Algorithm

Lesson - 32

Your One-Stop Solution to Understand Recursive Algorithm in Programming

Lesson - 33

The Definitive Guide to Understanding Greedy Algorithm

Lesson - 34

Your One-Stop Solution to Understand Backtracking Algorithm

Lesson - 35

The Fundamentals of the Bellman-Ford Algorithm

Lesson - 36

Your One-Stop Solution for Graphs in Data Structures

Lesson - 37

The Best Guide to Understand and Implement Solutions for Tower of Hanoi Puzzle

Lesson - 38

A Simplified and Complete Guide to Learn Space and Time Complexity

Lesson - 39

All You Need to Know About the Knapsack Problem : Your Complete Guide

Lesson - 40

The Fibonacci Series: Mathematical and Programming Interpretation

Lesson - 41

The Holistic Look at Longest Common Subsequence Problem

Lesson - 42

The Best Article to Understand What Is Dynamic Programming

Lesson - 43

A Guide to Implement Longest Increasing Subsequence Using Dynamic Programming

Lesson - 44

A Holistic Guide to Learn Stop Solution Using Dynamic Programming

Lesson - 45

One Stop Solution to All the Dynamic Programming Problems

Lesson - 46

Understanding the Fundamentals of Binomial Distribution

Lesson - 47

Here’s All You Need to Know About Minimum Spanning Tree in Data Structures

Lesson - 48

Understanding the Difference Between Array and Linked List

Lesson - 49

The Best Article Out There to Understand the B+ Tree in Data Structure

Lesson - 50

A Comprehensive Look at Queue in Data Structure

Lesson - 51

Your One-Stop Solution to Understand Coin Change Problem

Lesson - 52

The Best Way to Understand the Matrix Chain Multiplication Problem

Lesson - 53

Your One-Stop Solution to Learn Floyd-Warshall Algorithm for Using Dynamic Programming

Lesson - 54

The Best Tutorial You'll Ever Need for Queue Implementation Using Linked List

Lesson - 55
Understanding the Fundamentals of Binomial Distribution

Probability and statistics have enormous applications in data science, with artificial intelligence and machine learning relying heavily on them. In this article, you will learn Binomial Distribution, an essential part of the probability function.

What Is a Random Variable?

A random variable is a variable whose value is not known. It can either be discrete (having a specific value) or continuous (any value in a continuous range). All possible values that a random variable accepts is also called a sample space.

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What Is a Binomial Random Variable?

A binomial random variable is a number of successes in an experiment consisting of N trails. Some of the examples are:

  • The number of successes (tails) in an experiment of 100 trials of tossing a coin. Here the sample space is {0, 1, 2, …100}
  • The number of successes (four) in an experiment of 100 trials of rolling a dice. Here the sample space is {0, 1, 2, …100}

What Is Binomial Distribution?

In a binomial experiment, the binomial distribution is a discrete probability distribution that represents the probabilities of binomial random variables. The binomial distribution is a probability distribution associated with a binomial experiment in which the binomial random variable specifies the number of successes or failures that occurred within that sample space.

Let’s take an example. Suppose you flipped a coin. The probability of getting heads or tails is equal. But what will be the probability of getting six heads in ten flips of coins? This is where you will need binomial distribution. You can calculate the probability of getting six heads in ten flips of a coin.

The binomial distribution formula for any random variable X is given by

P(x, n, P) = nCx * Px * (1 - P)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, … (total number of successes)

p = Probability of success in a single experiment

Let’s calculate the probability of getting exactly six heads when a coin is tossed ten times.

We will use the formula, P(x, n, P) = nCx * Px * (1 - P)n-x  

where n = 10, p = 0.5, x = 6

P(x=6) = 10C6 * 0.56 * 0.54 = 0.205

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Mean and Variance of Binomial Distribution

The mean and variance of the binomial distribution are: 

Mean = np

Variance = npq

where,

p is the probability of success 

q is the probability of failure (1-p)

n is the number of trials.

Properties of Binomial Distribution

The properties of a binomial distribution are:

  1. There are only two possible outcomes: True or False, Yes or No.
  2. There are N number of independent trials.
  3. The probability of success and failure varies in each trial.
  4. Only the number of successes are taken into account out of N independent trials.

Binomial Distribution Python: Example

Let’s analyze the following python example to get an idea of the binomial distribution. 

Binomial_Distribution_1

  • Here N is the number of trials, and p is the probability of getting success in each trial.
  • The binomial random variable, X, shows the number of successes in each experiment.

The output plot that you will get after executing the code is shown below.

Binomial_Distribution_2

If you consider the above graph, the probability of getting success is 0.175.

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Conclusion

In this “Understanding the Fundamentals of Binomial Distribution“ article, you have learned about Binomial Distribution and its properties along with an example to better understand the concept. 

If you are keen on learning about Binomial Distribution and related statistical concepts, you could explore a career in data analytics. Simplilearn’s Post Graduate Program in Data Analytics is one of the most comprehensive online programs for Data Analytics. 

If you have any questions or queries related to this tutorial or our certification course, let us know in the comments section of this article, and our experts will be happy to answer. 

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Simplilearn is one of the world’s leading providers of online training for Digital Marketing, Cloud Computing, Project Management, Data Science, IT, Software Development, and many other emerging technologies.

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