Binomial VS Bernoulli Distribution!



Original Source Here

Binomial Distribution!

It is the collection of Bernoulli trials for the same event, i.e., it contains more than 1 Bernoulli event for the same scenario for which the Bernoulli trial is calculated.

Way to represent Binomial Distribution!

It can be represented using two things:

  1. The number of Bernoulli trials.
  2. Probability of an event in each trial.
Binomial Distribution representation! [Image by Author]

In the image above, “n” corresponds to the number of Bernoulli trials, & “p” corresponds to the probability of the event in each trial.

Probability Function to calculate Binomial Distribution!

When there is a requirement to calculate the likelihood of the occurrence of some event a specific number of times out of a fixed number of times, the formula listed below is used.

Probability Function for Binomial Distribution! [Image by Author]

In the above equation:

  • “n” is the total number of trials of an event.
  • “s” corresponds to the number of times an event should occur.
  • “p” is the probability that the event will occur.
  • “(1 — p)” is the probability that the event will not occur.
  • “C” term is for combinations.

Example of Binomial Distribution!

Considering the same example of the Bernoulli Distribution, let’s create Binomial Distribution from that example.

Considering 95% & 5% for passing & failing an exam for a student respectively. If we want to calculate the probability of a student to pass exactly 5 exams out of 5 exams in which it appeared, using the above probability formula it can be easily calculated.

According to the situation:
n = 5,
s = 5,
p = 0.95,
(1 — p) = 0.05

The number of ways to select 5 out of 5 is 1, so the first term of the formula becomes 1, now we have:

probability(student pass all 5 exams) = 1 * (0.95)^(5) * (0.05)(0)
=> 0.774

Therefore, there is approximately a 77.4 % chance, that the student passes all of the 5 exams.

AI/ML

Trending AI/ML Article Identified & Digested via Granola by Ramsey Elbasheer; a Machine-Driven RSS Bot



via WordPress https://ramseyelbasheer.wordpress.com/2020/12/31/binomial-vs-bernoulli-distribution/

Popular posts from this blog

The 2021 machine learning, AI, and data landscape

Image
https://venturebeat.com/wp-content/uploads/2020/03/AI_winter-e1591205079457.jpg?w=1200&strip=all Original Source Here Just when you thought it couldn’t grow any more explosively, the data/AI landscape just did: the rapid pace of company creation, exciting new product and project launches, a deluge of VC financings , unicorn creation, IPOs, etc. It has also been a year of multiple threads and stories intertwining. One story has been the maturation of the ecosystem, with market leaders reaching large scale and ramping up their ambitions for global market domination, in particular through increasingly broad product offerings. Some of those companies, such as Snowflake, have been thriving in public markets (see our MAD Public Company Index ), and a number of others (Databricks, Dataiku, DataRobot, etc.) have raised very large ( or in the case of Databricks, gigantic ) rounds at multi-billion valuations and are knocking on the IPO door (see our Emerging MAD company Index ). But...
Read more

Fully Explained DBScan Clustering Algorithm with Python

Image
Original Source Here Fully Explained DBScan Clustering Algorithm with Python Unsupervised learning in machine learning on density-based clusters Clustering In unsupervised Learning. A photo by Author In this article, we will discuss the machine learning clustering-based algorithm that is the DBScan cluster. The approach in this cluster algorithm is density-based than another distance-based approach. The other cluster which is distance-based looks for closeness in data points but also misclassifies if the point belongs to another class. So, density-based clustering is suited in this kind of scenario. The cluster algorithms come in unsupervised learning in which we don’t rely on target variables to make clusters. In a cluster, the main concern is on maximum dense connected points. The density-based clustering can be useful in arbitrary shapes even with noise. The working function of the density-based cluster is shown below: We select a random data point. Then it will ...
Read more

Hierarchical clustering explained

Image
Original Source Here Interpretation of dendrogram Each level of dendrogram has a subtle meaning to the relationship between its data members. In a regular relationship chart, one may interpret that at the top lies grandparents or the first generation, the next level corresponds to parents or second generation and the final level belongs to children or third generation. Likewise, in every branching procedure of dendrogram, all the data points having the membership at each level belongs to a certain class. However, to infer this class entity, one has to go through a few individual samples of each level within the formulated cluster and find out what feature is common in the resulting cluster. Also, these inferred classes need not be similar at the sister branches. For example, in level 2, the cats have been clustered on big ears and calm behavior but dogs have been clustered on a similar attribute of size. Inferred classes of data in dendrogram by the user (Image by Author) C...
Read more