# Physics307L:People/Franco/Franco's Poisson Statistics

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## Poisson Statistics

SJK 13:41, 11 November 2008 (EST)
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)
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

Example w/ overlay--Steve Koch

### 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%
```