Asv

6.5 Statistics of measurements Table 6.1. Sample values of Poisson function P, x: 0 1 2 3 4 5 6 7a 89

m = 1 0.368 0.368 0.184 0.061 0.015 0.003 0.001 7E-5 9E-6 1E-6

m = 2 0.135 0.271 0.271 0.180 0.090 0.036 0.012 0.003 0.001 2E-4

m = 3 0.050 0.149 0.224 0.224 0.168 0.101 0.050 0.022 0.008 0.003

m = 4b 0.018 0.073 0.147 0.195 0.195 0.156 0.104 0.060 0.030 0.013

m = 6c 0.002 0.015 0.045 0.089 0.134 0.161 0.161 0.138 0.103 0.069

m = 10d 5E-5 5E-4 0.002 0.008 0.019 0.038 0.063 0.090 0.113 0.125

a The notation 7E-5 indicates 7x 10 5.

b The values of Px for m = 4 at x = 10 and 11 are 0.005 and 0.002 respectively. c The values of Px for m = 6 at x = 10-14 are 0.041, 0.023, 0.011,0.005, 0.002. d The values of Px for m = 10 at x = 10-18 are: 0.125, 0.114,0.095,0.073,0.052, 0.035, 0.022, 0.013,0.007.

Normal distribution

One can describe a continuous and symmetrical normal distribution, also known as the Gaussian distribution, even though Gauss's derivation (1809) was preceded by LaPlace's (1774) and DeMoivre's (1735). It gives the differential probability dPx of finding the value x within the differential interval dx,

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