# User:Manuel Franco Jr./Notebook/Physics Lab 307/2008/10/15 Poisson Statistics Lab Main project page Previous entry      Next entry # Poisson Statistics

Lab Partner: David

Source of Raw Data 

## Objective

"This simple experiment will help you gain familiarity with the second most important statistical distribution in physics, the Poisson distribution." (Lab Manual Section 8.1)

## Materials

1. Scintillator with NaI (Sodium Iodide) crystals 
2. PMT
3. High Voltage Power Source(1000V to 2000V) 
4. A Cave of Lead bricks 
5. A MCA (MultiChannel Analyzer) card inside a computer
6. A Computer
7. BNC Cables
8. A "hydra" breakout cable 

## Connections

The PMT is connected to the scintillator as one unit. From there, the PMT is connect to two other inputs. One is connected to the power supply, and the other is connected to the MCA card in the computer. The computer has a program that measures the counts per time. The power supply was set in between 1000V and 2000V. The computer should be on and your almost ready to go.

## Procedure

The process of taking the data is pretty simple once all the connections are in the right place and the correct program is running. Turn on the apparatus. At this point you have to learn how the use the program. After learning the basics, I just let the computer do the plotting, sit back and wait. The manual and lab overview in the Lab page have details on the computer program, (ask Koch). The NaI will emit particles photons and the PMT will count them over a time period using the process. Gather the data.

## Data

All my data and graphs are in this worksheet. Poisson Worksheet

SJK 12:17, 11 November 2008 (EST) 12:17, 11 November 2008 (EST)
I thought we spent time doing some counts by hand (with Aram using his stopwatch), and had a whole bunch of discussion about the standard deviation of the data being different than what it should be...I don't see any notes about any of that!

## Data Analysis

In experiments the emitted particles are independent of time. They are events counted at random but at a constant rate. The Poisson distribution is a probability function that suits this condition. When the mean is high it takes the shape of a Gaussian curve, but when it is small it looks like graph Poisson 10 in the worksheet. After a certain Mean the normal distribution is fine.

X - "A Poisson random variable refers to the number of successes in a Poisson experiment." 

λ - "The average rate of success refers to the average number of successes that occur over a particular interval in a Poisson experiment." 

$p(k;\lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\!$ (k or n) - "A Poisson probability refers to the probability of getting EXACTLY n successes in a Poisson experiment." 

$\lambda = \frac {\sum{x_i}}{N},$ - "A cumulative Poisson probability refers to the probability of getting AT MOST n successes in a Poisson experiment. Here, n would be a Poisson random variable."  SJK 12:15, 11 November 2008 (EST) 12:15, 11 November 2008 (EST)
I don't think your quotation about cumulative probability relates to your formula (which is just the best estimator for lambda)