Unit9BasicStatisticalAnalysisofRandomErrors（随机误差的统计学基本分析）Randomerrorsarethosevariablesthatremainaftermistakesaredetectedandeliminatedandallsystematicerrorshavebeenremovedorcorrectedfromthemeasuredvalues.（随机误差是在错误被察觉【detect】和消除【eliminate】后，并且所有系统误差被从测量值中移除或修正后，保留下的那些变量【variable变量、变化n.】）Theyarebeyondthecontroloftheobserver.（它们是观测者无法控制的）Sotherandomerrorsareerrorstheoccurrenceofwhichdoesnotfollowadeterministicpattern.（因此随机误差是不遵循某个确定性【deterministic确定性的】模式【pattern】而发生的误差）Inmathematicalstatistics,theyareconsideredasstochasticvariables,anddespitetheirirregularbehavior,thestudyofrandomerrorsinanywell-conductedmeasuringprocessorexperimenthasindicatedthatrandomerrorsfollowthefollowingempiricalrules:（在数理统计【mathematicalstatistics】中，它们被当成随机变量【stochasticvariable】，尽管它们的行为无规律，在任一正确的【well-conducted原意为品行端正的，这里指测量实验和活动是无误的】测量活动和实验中，对的随机误差的研究显示【indicate】随机误差遵循以下经验法则【empiricalrule】：）⑴Arandomerrorwillnotexceedacertainamount.（随即误差不会超过一个确定的值）⑵Positiveandnegativerandomerrorsmayoccuratthesamefrequency.（正负误差出现的频率相同）⑶Errorsthataresmallinmagnitudearemorelikelytooccurthanthosethatarelargerinmagnitude.（误差数值【magnitude量值、大小】小的比数值大的误差出现可能性大【belikelyto可能】）⑷Themeanofrandomerrorstendstozeroasthesamplesizetendstoinfinite.（当【as】样本大小【samplesize】趋近于无穷【infinite】时，随机误差的平均值趋近于0）Inmathematicalstatistics,randomerrorsfollowstatisticalbehaviorallawssuchasthelawsofprobability.（在数理统计中，随机误差遵循统计学的【statistical】行为【behavioral行为的】规律，如概率法则）Acharacteristictheoreticalpatternoferrordistributionoccursuponanalysisofalargenumberofrepeatedmeasurementsofaquantity,whichconformtonormalorGaussiandistribution.（发生在一个量的大量重复观测分析【analysisn.】中的误差分布的一个特征理论模式，遵照【conformto遵照】正态或高斯分布）【在对一个量进行大量重复观测分析后，得到一个误差分布的理论特征——正态或高斯分布】Theplotoferrorsizesversusprobabilitieswouldapproachasmoothcurveofthecharacteristicbell-shape.（误差大小与【versus与、与……的关系、与……相对】概率的关系图，接近一条光滑的特有的【characteristic特有的】钟形曲线。）Thiscurveisknownasthenormalerrordistributioncurve.（这条曲线被称为正态分布曲线）Itisalsocalledtheprobabilitydensityfunctionofanormalrandomvariable.（也叫做正态随机变量【normalrandomvariable】的概率密度【probabilitydensity】函数）Itisimportanttonoticethatthetotalareaoftheverticalbarsforeachplotequals1.（需特别注意的是，每个图的条形图总面积为1。）Thisistruenomatterthevalueofn(thenumberofsinglecombinedmeasurements),andthustheareaunderthesmoothnormalerrordistributioncurveisequalto1.（无论【nomatter】n（单一的联合的测量数目【独立观测数】）是多少，在光滑的误差正态分布曲线下的面积都是1。）Ifaneventhasaprobabilityof1,itiscertaintooccur,andthereforetheareaunderthecurverepresentsthesumofalltheprobabilitiesoftheoccurrenceoferrors.（如果一件事的概率为1，它一定会发生，因此曲线下方的面积代表了所有误差发生的概率。）Anumberofpropertiesthatrelatearandomvariableanditsprobabilitydensityfunctionareusefulinourunderstandingofitsbehavior.（有许多工具【property】与随机变量和它的概率密度函数有关，有助于我们理解...
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