The Poisson Distribution

A Blog on Probability and Statistics

Let $latex alpha$ be a positive constant. Consider the following probability distribution:

$latex displaystyle (1) P(X=j)=frac{e^{-alpha} alpha^j}{j!} j=0,1,2,cdots$

The above distribution is said to be a Poisson distribution with parameter $latex alpha$. The Poisson distribution is usually used to model the random number of events occurring in a fixed time interval. As will be shown below, $latex E(X)=alpha$. Thus the parameter $latex alpha$ is the rate of occurrence of the random events; it indicates on average how many events occur per unit of time. Examples of random events that may be modeled by the Poisson distribution include the number of alpha particles emitted by a radioactive substance counted in a prescribed area during a fixed period of time, the number of auto accidents in a fixed period of time or the number of losses arising from a group of insureds during a policy period.

Each of the above examples can…

View original post 704 more words

About schapshow

Math & Statistics graduate who likes gymnastics, 90s alternative music, and statistical modeling. View all posts by schapshow

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

Open source projects for neuroscience!

Systematic Investor

Systematic Investor Blog

Introduction to Data Science, Columbia University

Blog to document and reflect on Columbia Data Science Class

Heuristic Andrew

Good-enough solutions for an imperfect world

"History doesn't repeat itself but it does rhyme"

My Blog

take a minute, have a seat, look around

Data Until I Die!

Data for Life :)

R Statistics and Programming

Resources and Information About R Statistics and Programming

Models are illuminating and wrong

Data & Machine Learning & Product

Xi'an's Og

an attempt at bloggin, nothing more...

Practical Vision Science

Vision science, open science and data analysis

Big Data Econometrics

Small posts about Big Data.

Simon Ouderkirk

Remote Work, Small Data, Digital Hospitality. Work from home, see the world.


Quantitative research, trading strategy ideas, and backtesting for the FX and equity markets


I can't get no

The Optimal Casserole

No Line Is Ever Pointless

SOA Exam P / CAS Exam 1

Preparing for Exam P / Exam 1 thru Problem Solving


Mathematical statistics for the layman.

%d bloggers like this: