基本統(tǒng)計(jì)學(xué)課件

基本統(tǒng)計(jì)學(xué)彭成煌基本統(tǒng)計(jì)學(xué)1●母體,群體(Population):研究者所欲研究的全部對(duì)象所成之集合樣本(Sample):母體的部分集合●參數(shù),母數(shù)(Parameter):描述母體的特徵量數(shù)統(tǒng)計(jì)量(Statistic):描述樣本的特徵量數(shù)●母體,群體(Population):2抽樣(Sampling)推論(inference)PopulationParameterSampleStatisticPopulationsizeNSamplesizen抽樣(Sampling)推論(inference)Popul3觀測(cè)值(Observations):X1,X2,…,Xn

●位置量數(shù)(Locationmeasures),集中趨勢(shì)量數(shù)(Measuresofcentraltendency)

●差異量數(shù)(Dispersionmeasures)有序統(tǒng)計(jì)量(OrderStatistics):X(1),X(2),…,X(n)

觀測(cè)值(Observations):X1,X2,4●位置量數(shù):2.中位數(shù)(Median)1.平均數(shù)(Mean)(統(tǒng)計(jì)量)(參數(shù))3.眾數(shù)(Mode)●位置量數(shù):2.中位數(shù)(Median)1.平均數(shù)(M54.百分位數(shù)(Percentile)第k百分位數(shù)(k-thPercentile)whereNote:10.Samplesizen=504.百分位數(shù)(Percentile)第k百分位數(shù)(k-t630.四分位數(shù)(Quartile)Q1=P25,Q2=P50=Md

,Q3=P75

40.十分位數(shù)(Deciles)D1=P10,D2=P20,…,D9=P9020.P50=Md30.四分位數(shù)(Quartile)Q1=P25,7●差異量數(shù)1.全距(Range)R=X(n)-X(1)2.四分位距(Interquartile-range)IQR=Q3-Q13.四分位差(Quartiledeviation)Q.D.=IQR/2(=Q2-Q1=Q3-Q2

,對(duì)稱資料)●差異量數(shù)1.全距(Range)2.四分位距(Interq84.平均絕對(duì)偏差(MeanAbsoluteDeviation)6.標(biāo)準(zhǔn)差(StandardDeviation)(統(tǒng)計(jì)量)(參數(shù))5.變異數(shù)(Variance),4.平均絕對(duì)偏差(MeanAbsoluteDeviati97.變異係數(shù)(CoefficientofVariation)例1.成人v.s.小孩之體重(統(tǒng)計(jì)量)(參數(shù))

樣本數(shù)平均數(shù)標(biāo)準(zhǔn)差C.V.成人16057.011.019.3%小孩185.61.425.0%7.變異係數(shù)(CoefficientofVariatio10例2.某一群小孩之身高、體重如下表

平均數(shù)標(biāo)準(zhǔn)差C.V.身高1201512.5%體重25520.0%例2.某一群小孩之身高、體重如下表

平均數(shù)標(biāo)準(zhǔn)差C.V.11隨機(jī)變數(shù)及機(jī)率分配隨機(jī)變數(shù)12●隨機(jī)變數(shù)(RandomVariable,r.v.)例.丟一公正銅板2次HH,HT,TH,TTSamplespaceHHHTTHTT210SX(S)XX:numbersof“H”r.v.X之可能值0,1,2●隨機(jī)變數(shù)(RandomVariable,r.v.)例.13丟一公正銅板2次,X:numbersof“H”

HHHTTHTT210SX(S)X1/42/41/4f(x)f●機(jī)率分配函數(shù)(Probabilitydistributionfunction)丟一公正銅板2次,X:numbersof“H”14i.e.x012Totalf(x)=P(X=x)1/42/41/41ori.e.x012Totalf(x)=P(X=x)1/42/4152.若r.v.X之可能值有xi,i=1,2,…,k,則f(xi)滿足(i)(ii)1.f(x)=P(X=x)Note:●累積機(jī)率函數(shù)(Cumulativeprobabilityfunction)Note:Ifaandbareconstants,a<b,then2.若r.v.X之可能值有xi,i=1,16r.v.可分為:

(i)離散型或間斷型(Discretetype)

(ii)連續(xù)型(Continuoustype)例:1.擲一公正骰子,r.v.X表骰子點(diǎn)數(shù)2.箱子中有6紅、4白球,採(cǎi)“取後放回”方式連續(xù)抽5球,

r.v.Y表紅球個(gè)數(shù)3.以r.v.Z表示,某路口去年發(fā)生交通事故之次數(shù)4.以r.v.W表示,實(shí)驗(yàn)室人員的血壓5.以r.v.T表示,某廠牌日光燈壽命r.v.可分為:(i)離散型或間斷型(Discrete17

X-1.08332-0.62423-0.59418-0.08661-0.079920.031890.396580.513661.804822.23829

X18基本統(tǒng)計(jì)學(xué)課件19相對(duì)次數(shù)的平滑曲線:X之機(jī)率密度曲線f(x)(Probabilitydensitycurve,p.d.f.)相對(duì)次數(shù)的平滑曲線:20Note:1.2.3.4.5.(c.d.f.)Note:1.2.3.4.5.(c.d.f.)21●隨機(jī)變數(shù)X之期望值(Expectedvalue)與變異數(shù)期望值:(Discretetype)(Continuoustype)變異數(shù):Properties:(i)Ifaandbareconstants,(ii)Ifg(X)isafunctionofr.v.X,Properties:Ifaandbareconstants,●隨機(jī)變數(shù)X之期望值(Expectedvalue)與變22例.擲一公正骰子,以r.v.X表其出現(xiàn)點(diǎn)數(shù),則X之期望值變異數(shù)例.擲一公正骰子,以r.v.X表其出現(xiàn)點(diǎn)數(shù),則23H.W.丟一公正銅板3次,並以r.v.Y表示“T”之次數(shù),試求1.Y之機(jī)率分配為何2.Y之mean、standarddeviation3.令

,則Z之mean、varianceH.W.丟一公正銅板3次,並以r.v.Y表示“T24Note:LetXandYbediscreterandomvariables,thejointprobabilitydistributionof(X,Y)isf(x,y),g(X,Y)isafunctionof(X,Y),then1.,2.themarginalprobabilitydistribution3.themeanofg(X,Y)isNote:LetXandYbedi254.where5.IfXandYareindependent,then(i)(ii)4.where5.IfXandYare26例.盒中有3藍(lán)、2紅及3白球,今隨機(jī)抽2球,令r.v.X表藍(lán)球數(shù)、Y表紅球數(shù)1.thejointprobabilitydistributionof(X,Y)P(1≦X+Y≦2)=f(0,1)+f(0,2)+f(1,0)+f(1,1)+f(2,0)=25/283.themarginalprobabilitydistributionare例.盒中有3藍(lán)、2紅及3白球,今隨機(jī)抽2球27例.擲一公正骰子10次,試求10次的點(diǎn)數(shù)和(S)之期望值與變異數(shù).解:令Xi