Physics307L:People/Franco/Franco's Poisson Statistics
From OpenWetWare
Jump to navigationJump to search
Poisson Statistics
SJK 13:41, 11 November 2008 (EST)
This summary is pretty thin...I understand that the lab took a bunch of time technically, but that doesn't mean you have to omit stuff that (I think) you learned about poisson. It's not enough to say it fits a normal distribution...you can put an overlay on your graph (as the example I added below). Also no mention of properties of the standard deviation, etc.
As the Mean increases
So as λ increases the Poisson distribution fits the Normal distribution.
SJK 13:39, 11 November 2008 (EST)
I see in your spreadsheets that you calculate the Poisson distribution, but you do not multiply it by # channels and then overlay it on your graphs. See example below
Poisson Graphs from the spreadsheet from the lab were selected for simplicity: 4,6,7,8,9,10
λ=.3564 
λ=.6035 
λ=1.223 
λ=2.086 
λ=12.09 
λ=247.9 
Poisson Probability
There is a probability for the frequency of those events to occur. This is know as the Poisson Probability. Here are 3 examples. This is also on the Poisson Worksheet.
For Poisson Graph 4 Number Frequency Poisson Prob. 0 701 70.02% 1 282 24.96% 2 40 4.45% 3 1 0.53% 4 0 0.05% 5 0 0.00% 6 0 0.00% 7 0 0.00% 8 0 0.00% 9 0 0.00% 10 0 0.00%
For Poisson Graph 8 Number Frequency Poisson Prob. 0 46 12.42% 1 143 25.91% 2 145 27.02% 3 108 18.79% 4 45 9.80% 5 20 4.09% 6 4 1.42% 7 1 0.42% 8 0 0.11% 9 0 0.03% 10 0 0.01%
For Poisson Graph 9 Number Frequency Poisson Prob. 0 0 0.00% 1 0 0.01% 2 0 0.04% 3 0 0.17% 4 0 0.50% 5 3 1.21% 6 1 2.44% 7 7 4.21% 8 22 6.37% 9 30 8.55% 10 34 10.33% 11 32 11.35% 12 28 11.43% 13 24 10.63% 14 16 9.18% 15 18 7.39% 16 11 5.58% 17 8 3.97% 18 6 2.67% 19 6 1.70% 20 6 1.02% 21 1 0.59% 22 1 0.32% 23 1 0.17% 24 1 0.09% 25 0 0.04% 26 0 0.02% 27 0 0.01% 28 0 0.00% 29 0 0.00% 30 0 0.00%
