Question

7£®Ä³ÇøÒª½øÐÐÖÐѧÉúÀºÇò¶Ô¿¹Èü£¬ÎªÕù¶á×îºóÒ»¸öС×éÈüÃû¶î£¬¼×¡¢ÒÒ¡¢±ûÈýÖ§ÀºÇò¶ÓÒª½øÐбÈÈü£¬¸ù¾Ý¹æÔò£ºÃ¿Á½Ö§¶ÓÎéÖ®¼ä¶¼Òª±ÈÈüÒ»³¡£»Ã¿³¡±ÈÈüʤÕßµÃ3·Ö£¬¸ºÕßµÃ0·Ö£¬Ã»ÓÐƽ¾Ö£¬»ñµÃµÚÒ»ÃûµÄ½«¶áµÃÕâ¸ö²ÎÈüÃû¶î£®ÒÑÖªÒÒ¶Óʤ±û¶ÓµÄ¸ÅÂÊΪ$\frac{1}{5}$£¬¼×¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ$\frac{1}{6}$£¬ÒÒ¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ$\frac{1}{15}$£®
£¨¢ñ£©Çó¼×¶Ó·Ö±ðսʤÒҶӺͱû¶ÓµÄ¸ÅÂÊP₁£¬P₂£»
£¨¢ò£©ÉèÔڸôαÈÈüÖУ¬¼×¶ÓµÃ·ÖΪX£¬ÇóXµÄ·Ö²¼Áм°ÆÚÍû£®

Answer 1

·ÖÎö £¨1£©ÔĶÁµÃ³ö¶Ó»ñµÃµÚÒ»Ãû£¬Ôò¼×¶ÓʤÒÒ¶ÓÇҼ׶Óʤ±û¶Ó£¬¼×¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ${P_1}¡Á{P_2}=\frac{1}{6}$£» ÒÒ¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ$£¨1-{P_1}£©¡Á\frac{1}{5}=\frac{1}{15}$£¬Çó½â·½³Ì×é¼´¿É£®
£¨2£©¸ù¾ÝÌâÒâµÃ³öX¿ÉÄÜÈ¡µÄֵΪ£º0£¬3£¬6£¬·Ö±ðÇó³ö¸ÅÂʵóö·Ö²¼Áм´¿É£¬Çó½âÊýѧÆÚÍû£®

½â´ð ½â£º£¨¢ñ£©ÓÉÌâÒ⣬¼×¶Ó»ñµÃµÚÒ»Ãû£¬Ôò¼×¶ÓʤÒÒ¶ÓÇҼ׶Óʤ±û¶Ó£¬
¡à¼×¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ${P_1}¡Á{P_2}=\frac{1}{6}$£»     ¢Ù
ͬÀí£ºÒÒ¶Ó»ñµÃµÚÒ»ÃûµÄ¸ÅÂÊΪ$£¨1-{P_1}£©¡Á\frac{1}{5}=\frac{1}{15}$£®¢Ú
Óɢ٢ڵãº${P_1}=\frac{2}{3}£¬{P_2}=\frac{1}{4}$£®
ËùÒԼ׶ÓսʤÒҶӵĸÅÂÊΪ$\frac{2}{3}$£¬¼×¶Óսʤ±û¶ÓµÄ¸ÅÂÊ$\frac{1}{4}$£®
£¨¢ò£©$P£¨X=0£©=£¨1-\frac{2}{3}£©£¨1-\frac{1}{4}£©=\frac{1}{4}$£»
$P£¨X=3£©=\frac{2}{3}£¨1-\frac{1}{4}£©+£¨1-\frac{2}{3}£©\frac{1}{4}=\frac{7}{12}$£»
$P£¨X=6£©=\frac{2}{3}¡Á\frac{1}{4}=\frac{1}{6}$£®
XµÄ·Ö²¼ÁÐΪ£º

X	0	3	6
P	$\frac{1}{4}$	$\frac{7}{12}$	$\frac{1}{6}$

$E£¨X£©=0¡Á\frac{1}{4}+3¡Á\frac{7}{12}+6¡Á\frac{1}{6}=\frac{11}{4}$£®

µãÆÀ ±¾Ì⿼²ìÁ˹ŵä¸ÅÂÊÔÚʵ¼ÊÎÊÌâÖеÄÓ¦Ó㬿¼²ìÁËѧÉúµÄÔĶÁ·ÖÎöÄÜÁ¦£¬¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮