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Mean values and rms fluctuations. Every day for 20 days I counted the number of spiders in my office and recorded the following daily populations: 2, 8, 2, 6, 3, 5,7, 2, 2, 7, 5, 8, 6, 3, 5, 8, 0, 9, 3,1 (a) Find the mean population (or ф ) defined by where i is the J measurement and N is the total number of measurements. (b) For statistical mechanics, a more useful (but equivalent) definition of the populations mean value (or expected value) is as follows:

where P(d) is the probability for population ф to occur. Estimate the probabilities P(H) for all possible values of the spider population 9 (c) Find the root-mean-square (rms) fluctuation in the spider population, Дф This is a common measure of variability defined as the square root of the mean square fluctuations, where the mean square fluctuations are given by: or more generally by: (d) From either definition of (Δ)2, derive the general formula and verify that it is satisfied here. (Way is the mean satisfied here. (1? 7 is the mean 2 value of φ-.)

math   Statistics-And-Probability   
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soited beto 0,1,93,,,55,, 6,,1,, 8,,9, 9 0+12 J-1 20 서)= 92-4.c Уго -o.os 2 %,-0-15 920 : 0 4 0 IS 2/20o 2 3/0 :0.15 2o Nouw

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