Question

14£®Ä³³ÇÊÐËæ»ú¼à²âÒ»ÄêÄÚ100ÌìµÄ¿ÕÆøÖÊÁ¿PM2.5µÄÊý¾ÝAPI£¬½á¹ûͳ¼ÆÈçÏ£º

API	[0£¬50]	£¨50£¬100]	£¨100£¬150]	£¨150£¬200]	£¨200£¬250]	£¨250£¬+¡Þ£©
ÌìÊý	6	12	22	30	14	16

£¨1£©Èô½«APIÖµµÍÓÚ150µÄÌìÆøÊÓΪ¡°ºÃÌ족£¬²¢½«ÆµÂÊÊÓΪ¸ÅÂÊ£¬¸ù¾ÝÉÏÊö±í¸ñ£¬Ô¤²â½ñÄê¸ß¿¼6ÔÂ7ÈÕ¡¢8ÈÕÁ½ÌìÁ¬Ðø³öÏÖ¡°ºÃÌ족µÄ¸ÅÂÊ£»
£¨2£©APIÖµ¶Ô²¿·ÖÉú²úÆóÒµÓÐ×ÅÖØ´óµÄÓ°Ï죬¼ÙÉèijÆóÒµµÄÈÕÀûÈóf£¨x£©ÓëAPIÖµxµÄº¯Êý¹ØϵΪ£ºf£¨x£©=$\left\{\begin{array}{l}40£¨x¡Ü150£©\\ 15£¨x£¾150£©\end{array}$£¨µ¥Î»£»ÍòÔª£©£¬ÀûÓ÷ֲã³éÑùµÄ·½Ê½´Ó¼à²âµÄ100ÌìÖÐÑ¡³ö10Ì죬ÔÙ´ÓÕâ10ÌìÖÐÈÎÈ¡3Ìì¼ÆËãÆóÒµÀûÈóÖ®ºÍX£¬ÇóÀëÉ¢ÐÍËæ»ú±äÁ¿XµÄ·Ö²¼ÁÐÒÔ¼°ÊýѧÆÚÍûºÍ·½²î£®

Answer 1

·ÖÎö £¨1£©¸ù¾Ý·Ö²¼±í¸ñµÃ³öÐøÁ½Ìì³öÏÖ¡°ºÃÌ족µÄ¸ÅÂÊ£®
£¨2£©È·¶¨XµÄËùÓпÉÄÜȡֵΪ45£¬70£¬95£¬120£¬ÀûÓöþÏî·ÖµÄ¸ÅÂÊ֪ʶÇó½â$P£¨X=70£©=C_3^1¡Á0.4¡Á{£¨0.6£©^2}=0.432$£¬$P£¨X=95£©=C_3^2¡Á{£¨0.4£©^2}¡Á0.6=0.288$£¬P£¨X=120£©=£¨0.4£©³=0.064£¬¸ù¾ÝÀûÓ÷ֲ¼ÁÐÇó½âE£¨X£©£¬D£¨X£©£®

½â´ð ½â£º£¨1£©¸ù¾Ýͳ¼ÆÊý¾Ý³öÏÖºÃÌìµÄ¸ÅÂÊΪ0.4£¬
ÔòÁ¬ÐøÁ½Ìì³öÏÖ¡°ºÃÌ족µÄ¸ÅÂÊΪ0.4¡Á0.4=0.16£®
£¨2£©XµÄËùÓпÉÄÜȡֵΪ45£¬70£¬95£¬120
£®P£¨X=45£©=£¨0.6£©³=0.216
$P£¨X=70£©=C_3^1¡Á0.4¡Á{£¨0.6£©^2}=0.432$
$P£¨X=95£©=C_3^2¡Á{£¨0.4£©^2}¡Á0.6=0.288$
P£¨X=120£©=£¨0.4£©³=0.064

X	45	70	95	120
P	0.216	0.432	0.288	0.064

E£¨X£©=45¡Á0.216+70¡Á0.432+95¡Á0.288+120¡Á0.064=75
D£¨X£©=£¨45-75£©²¡Á0.216+£¨70-75£©²¡Á0.432+£¨95-75£©²¡Á0.288+£¨120-75£©²¡Á0.064=450

µãÆÀ ±¾Ð¡ÌâÖ÷Òª¿¼²éͳ¼ÆÓë¸ÅÂʵÄÏà¹Ø֪ʶ£¬ÆäÖаüÀ¨¸ÅÂʵÄÇ󷨡¢ÀëÉ¢ÐÍËæ»ú±äÁ¿µÄÊýѧÆÚÍûÒÔ¼°·½²î£®±¾ÌâÖ÷Òª¿¼²éѧÉúµÄÊý¾Ý´¦ÀíÄÜÁ¦ºÍÔËËãÇó½âÄÜÁ¦£®