隨機(jī)向量的函數(shù)及其應(yīng)用趙樹杰PPT學(xué)習(xí)教案

1、會計(jì)學(xué)1隨機(jī)向量的函數(shù)及其應(yīng)用趙樹杰隨機(jī)向量的函數(shù)及其應(yīng)用趙樹杰第1頁/共47頁第2頁/共47頁X)(XgY YXX)(xf)(XXxY)(yf)(xgy)(yhx y第3頁/共47頁.1)1 (其他0)()(YYyJyhxfyfyyhJd)(d.2)1 (|XXYxxg),(minXXYxxg),(max第4頁/共47頁),(2XXNXXXXYYXXxy/ )( XXyxXXXyyJd/ )( d2exp21)(221yyf) 1 , 0(NY第5頁/共47頁X其他常數(shù)）0, 0(|11)(2aaxaxaaxf0X6/22aXcXYcYcxycyx1J第6頁/共47頁Y其他常數(shù)）0, 0(|

2、11)(2acaycacyaayfcY6/22aY)(xf)(yfY第7頁/共47頁a / 1aa0caca)(xf)(yfc)(xf)(yf)2(aca) 6/()(acYZ0Z12ZZ第8頁/共47頁) 1 , 0 (X2XYY2xy21yx )2/(1|21yJ 00021)(212121yyyxfyxfyyf第9頁/共47頁0002exp21)(21yyyyyf)(xfY12)(yf0y21N第10頁/共47頁)(XgYYXcXYccXY)(yf)(xfcYYX)(XgYYX第11頁/共47頁)(XgYYxxfyyfd)(d)(Y2Y)(yfYYyyyfYd)(YYyyfyYYd)()

3、(22)(xgy) 3 . 1 () 4 . 1 (第12頁/共47頁)(yfXXxxfxgYd)()(XXxxfxgYYd)()(22) 5 . 1 () 6 . 1 () 3 . 1 () 4 . 1 ()(XgY Y2YYX)(xfkXXxxfxgykYykd)()()(E) 7 . 1 (第13頁/共47頁2exp21)(221xxf) 1 , 0 (X2XYY2Y0002exp21)(21yyyyyf第14頁/共47頁YY2YyyyyyyyfYd2exp21d)(0210121212121d2exp212102121yyy1d2exp21)(E0212222yyyyyYY1d2exp

4、2102321yyy212521212521第15頁/共47頁YY2YxxxxxfxYd2exp21d)(2212202221d2exp221xxx1212121221221xxfxgYYd)()(22xxxd2exp2112212221221222321221第16頁/共47頁Nknshxkkkk, 2 , 1|第17頁/共47頁T21)(NXXXXN)(XgYXY),(21NxxxfNNXNY),(21NyyyfNNN第18頁/共47頁NkxxxgyNkk, 2 , 1),(21) 1 . 2 (), 2 , 1(Nkyk|)(,),(),(2211JhxhxhxfNNNkyyyhxNkk

5、, 2 , 1),(21) 2 . 2 ()(kkhx),(21Nyyyf) 3 . 2 (NJN第19頁/共47頁) 4 . 2 (NNNNNNyhyhyhyhyhyhyhyhyhJ)()()()()()()()()(212222111211N第20頁/共47頁Tttnatstx0)(),()(；)(tx)cos(),(0taats ；)(af)(f)(tn2)(0NPnQIjxx 第21頁/共47頁)(lf0)(212Q2Ilxxl20)arctan(IQxx)(f)(lf)(f第22頁/共47頁200cosIllxl200sinQllx),|(Iaxf),|(Qaxf),|,(QIaxx

6、f),|, (alf),|(alf),|(af0)(llf20)(f第23頁/共47頁NT21)(NaaaaNT21)(NXXXXNkkkXaX1TXa) 1 . 3 (T21)(NXXXXN第24頁/共47頁NT21)(NXXXX) 2 . 3 (T)(21NXXXXT)(EXXXXXC) 3 . 3 ()()(21exp|)2(1),(1T21221XXXXxCxCNNxxxf) 4 . 3 (NN第25頁/共47頁T21)(NXXXXN) 5 . 3 (NkkkXaX1XXNkXkXkaX1)(E) 6 . 3 (XXkXkX)(E22)(EkkXXkX第26頁/共47頁) 8 . 3

7、() 9 . 3 (XXiXjXNjiXXjiXXXjXiijjiji, 2 , 1,)(EX2)(E112NkNkXkkkXkaXajikXNkNiXijjNjiXkaaaij11122iXjX) 0(ij2122kXNkkXa)10. 3 (第27頁/共47頁)11. 3 (NkXXaXNkkkk, 2 , 11TXaXT21)(Naaaak1ka), 2 , 1(0kjNjaj；), 2 , 1(NkXkXN1 (M)NM N第28頁/共47頁T21)(NXXXXNN第29頁/共47頁N) 4 . 3 (XC21|XC1XC)(),(121NkkNxfxxxf)11. 3 ()(kxfk

8、X第30頁/共47頁NNkXXkNXNxxxxf12222212)(exp21),()12. 3 (XkX), 2 , 1(22NkXXkN)IID(第31頁/共47頁)13. 3 (NMT21)(NXXXXNAAXYMYMjYj(), 2 , 1(NkXk), 2 , 1M), 2 , 1(MjYjX第32頁/共47頁)14. 3 (MjjjYaY1TYaMXT21)(MaaaaYYYYMYYCYXYA TAACCXY)15. 3()16. 3(第33頁/共47頁)17. 3(22X)(xfXjeX)(XGxxfGxXde )()(jX)(xf)(XGde )(21)(j xXGxf)18.

9、 3(第34頁/共47頁N22kXNkXkXk, 2 , 1)E(Nk2kXY1a), 2 , 1(2NkXYkkNkXXk, 2 , 122222222122 j1)2/(exp2exp2 j11)(XXXXXXYkkkGNk, 2 , 1 )19. 3(第35頁/共47頁2)(kYG, 2 , 1( kYk2221212222 j1)2/(exp2exp2 j11)(XXXNkXNkXNXYkkG)20. 3(N),N)(YGNkkNkkXYY121第36頁/共47頁2)21. 3()j(1expj1IFTaban02exp)(21211212ybyIaybynnnIn02exp0021)

10、(22112122121222yyIyyyyfXNkXNXNkXNkXNXkkk)22. 3(第37頁/共47頁202exp0021)(22112122121222yyIyyyyfXNkXNXNkXNkXNXkkk)22.3(YN2NkXk12第38頁/共47頁2b)02exp0021)(22121222222yyNIyNyNyyfXXNXXXNX)23.3(YkX22XN), 2 , 1(NkkXX), 2 , 1(22NkkXXN第39頁/共47頁2c)0002exp) 2(21)(21222yyyNyyfXNNX)24.3(YkX20X22kXXN), 2 , 1(Nk第40頁/共47頁2d)0002exp) 2(21)(122yyyNyyfNN)25.3(YkX20X12XN), 2 , 1(Nk第41頁/共47頁第42頁/共47頁其他0)()(XXxxfxf)(XgY )(yhx Jyh)(其他0|)()(YYyJyhxfyfXXYxxg),(minXXYxxg),(max)()(xxf其他0| )(| )()(YYyyhyhfyf)(),(minggY)(),(maxggYYY第43頁/共47頁其他0)()(XXxxfxf)(XgY )(yhx