连续型随机变量及其密函数PPT学习教案

1、会计学1连续型随机变量及其密函数连续型随机变量及其密函数r.v X( )( ) , xF xf t dtx ( )0,f t X( )f t1,0( ) 0 , 0 xexF xxr.v XX1,0( ) 0 , 0 xexf xx( )( ) , xF xf t dtx ( )F xX第1页/共27页( )0f t ( )1f t dt211221()()( )xxP xXxF xF xf x dx12 xx( )f x( )( )f xF xyxO( )f x12 xxx( )f xyO12P xXx x( )f x0()( )( )limxF xxF xf xx 0limxP xXxxx

2、 x( )P xXxxf xx xxxxO( )f xyP xXxx第2页/共27页501000PX r.v X2,100( ) 0 ,100kxxf xx 1( )f x dx2100kdxx100k 100k , kX( )F x( )( )xF xf t dt2100100,100 0 , 100 xdt xtx1001,100 0 , 100 xxxX100050501000( )PXf x dx10002100dxx50100911100()100100010第3页/共27页XccxXc X. ,r v cP Xc 0 x 0P XcP cxXc ( )()F cF cx0 (0)x

3、 0P XcP aXbP aXbP aXbP aXb X. ,r v cXc0,P Xc第4页/共27页r.v XX( , )a b( , )XU a b ( )0f x , ( )badxf x dxba1( )f x( )f xOyx1b a ab ( ,)( , )c cLa bc LcdxP cXcLba1 ()LkLkbaba X( ,)c cLr.v X( , )a b( , )XU a bP Xc,c01,( ) 0 ,axbbaf x第5页/共27页,2XlXX2l XX(0,2 )Ul22XllXllXX /23 /2lXl /23 /2P lXl3 /2/212lldxl1

4、2X2lXl第6页/共27页x x55 ( 0.5 10,0.5 10)xxU第7页/共27页第8页/共27页1,0( ) 0 , 0 xexf xxr.v XX0( )XEXP ( )0f x 01xedx( )f x( )f x1Ox( )f x0 te dt1, ( )f x dxX( )( )xF xf t dt01,0 0 , 0txedt xx1,0 0 , 0 xexxxO 1( ) xF第9页/共27页1,0( ) 0 , 0 xexf xx1, 第10页/共27页( ), 0,0XEXPst|P Xst Xs,P Xst XsP XsP XstP Xs1/1/xs txsed

5、xedx()/s tsee/ te/1(1)te 1( )F t P Xt第11页/共27页Ot(0, tX(),0,1,2,!kttP Xkekk0,(),Xt Y0P YtP XteY( )1 (0)tF tP Ytet 1 ()YEXPY第12页/共27页22()21( ),2xf xex r.v XX,0, 2( ,) 2( ,)XN ( )0f x 22()21( )2xf x dxedx22()21()2xxed2212tedt1212( )f x第13页/共27页22()21( )2xf xe()()fxfx( )yf xxx,( )fxx,( )0,( )fxf x ( )f

6、xx1( )2flim( )lim( )0 xxf xf x( )yf xOx12xO( )f x2( )( )xfxf x 0,( )f xx2, : : : : 10.51.5第14页/共27页第15页/共27页人物介绍人物介绍第16页/共27页Ox-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8第17页/共27页( ) x222211( ), ( )22txxxexedt20,1(0,1)XNxxxO( )x( )x()x()1( )xx 第18页/共27页2( ,) , (0,1)XNXN 2( ,),XN (0,1)XZN( )ZFzP ZzZ XPzP

7、 Xz2()2212tzedt2212uzedu( ) z (0,1)ZN2( ,)XN ,tu:tz :uz 第19页/共27页70P X (50,100)XN; ;(60,16)XN.7050()10(2)0.977270P X 6700()4(2.5)0.9938 (60,16)60 (0,1)4XNXN (50,100)50 (0,1)10XNXN65P X 6550()10(1.5)0.933265P X 6560()4(1.25)0.8944 (60,16)60 (0,1)4XNXN (50,100)50 (0,1)10XNXN第20页/共27页2( ,),XN 22 33 PXP

8、XPX()/(0,1)XN PX 11XP (1)( 1) 2(1)1 0.682622 PX 22XP 2(2)1 0.954433 PX 33XP 2(3)1 0.99740.68260.95440.9974%26.6822%44.9533%74.99(3 ,3 ) 第21页/共27页42( ,(0.2) ). 4XN6.8 , 6.7 , 7.1 , 8.6.(6.86.77.18.6)/47.33|8.6| |8.67.33|1.270.633第22页/共27页, 1,2,kkpP Xxk12( ), ,p xP Xxxx x( ), f x dxP xXxdxx ( )p x( )f x dxr.v X( )f xr.v X1( )()1, ( )1kxkp xp xf x dx ( )( ) p xf x dx ( )( ) xp xf xdx( )f x 第23页/共27页12( ), ,f xP Xxxx xr.v X( )f xr.v X( )0, ( )1f xf x