1?2x???1?4x??113?2x?4x?xe?e??xe?e???? =???24??0???024422 £¨2£©E(2X1?3X2)?2E(X1)?3E(X2)?2?1?32??0x2?4e?4xdx
x?4x1?4x??352?4x?xe?e?e?1?? =1?3???2888??0 £¨3£©E(X1X2)?E(X1)?E(X2)?111?? 24813.[Ê®ËÄ] ½«nÖ»Çò£¨1¡«nºÅ£©Ëæ»úµØ·Å½ønÖ»ºÐ×Ó£¨1¡«nºÅ£©ÖÐÈ¥£¬Ò»Ö»ºÐ×Ó×°Ò»Ö»Çò¡£½«Ò»Ö»Çò×°ÈëÓëÇòͬºÅµÄºÐ×ÓÖУ¬³ÆÎªÒ»¸öÅä¶Ô£¬¼ÇXΪÅä¶ÔµÄ¸öÊý£¬ÇóE(X )
?1µÚiºÅºÐ×°µÚiºÅÇò½â£ºÒý½øËæ»ú±äÁ¿Xi??
0µÚiºÅºÐ×°·ÇiºÅÇò? i=1, 2, ? n ÔòÇòºÐ¶ÔºÅµÄ×ÜÅä¶ÔÊýΪX?XiµÄ·Ö²¼ÁÐΪ
¡à E(X)?E(
?Xi?1ni
Xi: P: 1 0
1 nnn?1 nE(Xi)1 ni=1, 2 ?? n
?Xi)??E(Xi)?n?i?1i?1n1?1 i=1, 2 ?? n n14.[Ê®Îå] ¹²ÓÐn°Ñ¿´ÉÏÈ¥Ñù×ÓÏàͬµÄÔ¿³×£¬ÆäÖÐÖ»ÓÐÒ»°ÑÄÜ´ò¿ªÃÅÉϵÄËø£¬ÓÃËüÃÇÈ¥ÊÔ¿ªÃÅÉϵÄËø¡£Éè³éȡԿ³×ÊÇÏ໥¶ÀÁ¢µÄ£¬µÈ¿ÉÄÜÐԵġ£Èôÿ°ÑÔ¿³×¾ÊÔ¿ªÒ»´Îºó³ýÈ¥£¬ÊÔÓÃÏÂÃæÁ½ÖÖ·½·¨ÇóÊÔ¿ª´ÎÊýXµÄÊýѧÆÚÍû¡£
£¨1£©Ð´³öXµÄ·Ö²¼ÂÉ£¬£¨2£©²»Ð´³öXµÄ·Ö²¼ÂÉ¡£ ½â£º£¨1£©
X P 1 2 3 ??n ??1 nn?11 ?nn?1n?1n?21 ??nn?1n?21 n1111?2???nn?1 ?2????n???nnnn2£¨2£©ÉèÒ»°ÑÒ»°ÑÔ¿³×µÄÊÔ¿ª£¬Ö±µ½°ÑÔ¿³×ÓÃÍê¡£
E(X)?1?
?iµÚi´ÎÊÔ¿ªÄÜ¿ªÃÅÉè Xi?? i=1, 2 ?? n
?0µÚi´ÎÊÔ¿ª²»ÄÜ¿ªÃÅÔòÊÔ¿ªµ½ÄÜ¿ªÃÅËùÐëÊÔ¿ª´ÎÊýΪX?Xi P i ?Xi?1ni
0 ¡ß
n?1n?211???? nn?1n?innnn?1 n1 ni=1, 2??n
E (Xi)=i?¡à E(X)?i12nn?1 ????????E(X)??nnnn2ii?1i?115. £¨1£©ÉèËæ»ú±äÁ¿XµÄÊýѧÆÚÍûΪE (X)£¬·½²îΪD (X)>0£¬ÒýÈëеÄËæ»ú±äÁ¿£¨X*³ÆÎª±ê×¼»¯µÄËæ»ú±äÁ¿£©£ºX*?ÑéÖ¤E (X* )=0£¬D (X* )=1
£¨2£©ÒÑÖªËæ»ú±äÁ¿XµÄ¸ÅÂÊÃܶȡ£
X?E(X)D(X)
?1?|1?x|,f(x)??,?0ÇóX*µÄ¸ÅÂÊÃܶȡ£ ½â£º£¨1£©E(X*)?E[0?x?2
ÆäËü,X?E(X)D(X)]?1D(X)[E(X)?E(X)]?0
2?X?E(X)?22
D (X* )= E [X*£E (X )* ]]= E (X* )= E??
??D(X)?? = £¨2£©E(X)?11E[X?E(X)]2??D(X)?1 D(X)DX?20x[1?|1?x|]dx?20?10x[1?(1?x)]dx??21x[1?(1?x)]dx?1
E(X2)?
?x2[1?|1?x|]dx??10x2[1?(1?x)]dx
??217x2[1?(1?x)]dx?6