15/88 3.2.3 Some Basic Statistics(统计学) 1.Probability Cumulative Probability (Continued) mumber of readings in an interval)/(total number of readings) .(3.1) Width of interval When the width of interval-→O,we have the probability density function概率密度函数： Z=f(x) And the probabilityofreadinglying betweena&p(a=f(x)dx(3.2) Cumulative distribution function(累积分布函数)：F(x)兰∫nf(x)dce ..(3.3) The most useful density function or distribution is the normal or Gaussian function: f0)=点aew-0/的 -0<X<+00 .(3.4) where u is the mean value and o is the standard deviation. 16/88 3.2.3 Some Basic Statistics(统计学) 2.Guassian Distribution ( Small value of o indicates a high Small probability that a“reading”wlbe found close to u. Gaussian distribution can never Large occur in the real world. In much practical work,Gaussian distribution is just assumed until Smallo troubles arise which justify a closer 1.0 study of the particular situation. 0.5 Figure 3.6 Gaussian Distribution o-defines the shape of the curve u-defines the position of the curve Figure 3.7 Non-Gaussian Distributionܼ ≜ (௡௨௠௕௘௥ ௢௙ ௥௘௔ௗ௜௡௚௦ ௜௡ ௔௡ ௜௡௧௘௥௩௔௟)/(௧௢௧௔௟ ௡௨௠௕௘௥ ௢௙ ௥௘௔ௗ௜௡௚௦) ௐ௜ௗ௧௛ ௢௙ ௜௡௧௘௥௩௔௟ … (3.1) When the width of interval → 0, we have the probability density function (概率密度函数) : ݔ ݂=ܼ ௫ ݔ݀ ݔ ݂ ׬ ≜ (ݔ)ܨ:(累积分布函数(function distribution Cumulative ିஶ … (3.3) The most useful density function or distribution is the normal or Gaussian function： ଵ) = ݔ)݂ ଶగ ఙ ݁ି ௫ିఓ మ/(ଶఙమ) −∞ < ݔ) ... ∞+ > 3.4) where μ is the mean value and σ is the standard deviation. And the probability of reading lying between ܽ & ܾ ≜ ݌>ܽ ݔ = ܾ>׬ ݂ ݔ݀ ݔ௕ ௔ … (3.2) 3.2.3 Some Basic Statistics(统计学) 1. Probability & Cumulative Probability (Continued) 15/88 Figure 3.6 Gaussian Distribution σ - defines the shape of the curve μ - defines the position of the curve Figure 3.7 Non-Gaussian Distribution 9 Small value of σ indicates a high probability that a “reading” will be found close to μ . 9 Gaussian distribution can never occur in the real world. 9 In much practical work, Gaussian distribution is just assumed until troubles arise which justify a closer study of the particular situation. 3.2.3 Some Basic Statistics(统计学) 2. GuassianDistribution 16/88