Question

16£®Ä³Å©¿ÆËù·¢ÏÖ£¬Ò»ÖÐ×÷ÎïµÄÄêÊÕ»ñÁ¿y£¨µ¥Î»£ºkg£©ÓëËü¡±Ïà½ü¡°×÷ÎïµÄÖêÊýx¾ßÓÐÏßÐÔÏà¹Ø¹Øϵ£¨ËùνÁ½Öê×÷ÎÏà½ü¡°ÊÇÖ¸ËüÃǵÄÖ±Ïß¾àÀë²»³¬¹ý1m£©£¬²¢·Ö±ð¼Ç¼ÁËÏà½ü×÷ÎïµÄÖêÊýΪ1£¬2£¬3£¬5£¬6£¬7ʱ£¬¸Ã×÷ÎïµÄÄêÊÕ»ñÁ¿µÄÏà¹ØÊý¾ÝÈçÏ£º

X	1	2	3	5	6	7
y	60	55	53	46	45	41

£¨¢ñ£©Çó¸Ã×÷ÎïµÄÄêÊÕ»ñÁ¿y¹ØÓÚËü¡±Ïà½ü¡°×÷ÎïµÄÖêÊýxµÄÏßÐԻع鷽³Ì£»
£¨¢ò£©Å©¿ÆËùÔÚÈçͼËùʾµÄÕý·½ÐεؿéµÄÿ¸ö¸ñµã£¨Ö¸×Ý¡¢ºáÖ±ÏߵĽ»²æµã£©´¦¶¼ÖÖÁËÒ»Öê¸Ã×÷ÎÆäÖÐÿһ¸öСÕý·½ÐεÄÃæ»ýΪ1£¬ÈôÔÚËùÖÖ×÷ÎïÖÐËæ»úÑ¡È¡Ò»Ö꣬ÇóËüµÄÄêÊÕ»ñÁ¿µÄ·Ö²¼ÁÐÓëÊýѧÆÚÍû£®£¨×¢£ºÄêÊÕ»ñÁ¿ÒÔÏßÐԻع鷽³Ì¼ÆËãËùµÃÊý¾ÝΪÒÀ¾Ý£©
¸½£º¶ÔÓÚÒ»×éÊý¾Ý£¨x₁£¬y₁£©£¬£¨x₂£¬y₂£©£¬¡­£¬£¨x_n£¬y_n£©£¬Æä»Ø¹éÖ±Ïßy=a+bxµÄбÂʺͽؾàµÄ×îС¶þ³Ë¹À¼Æ·Ö±ðΪ$\widehat{b}$=$\frac{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©£¨{y}_{i}-\overline{y}£©}{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©^{2}}$=$\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}•\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n•{\overline{x}}^{2}}$£¬$\widehat{a}$=$\overline{y}$-$\widehat{b}$$\overline{x}$£®

Answer 1

·ÖÎö £¨¢ñ£©¼ÆËã$\overline{x}$¡¢$\overline{y}$£¬Çó³ö»Ø¹éϵÊý£¬Ð´³ö»Ø¹é·½³Ì£»
£¨¢ò£©ÀûÓûعéÖ±Ïß¹ý³Ì£¬Çó³öx=2¡¢3¡¢4ʱ¶ÔÓ¦$\stackrel{¡Ä}{y}$µÄÖµ£»
¼ÆËã¶ÔÓ¦µÄ¸ÅÂÊÖµ£¬Ð´³ö·Ö²¼ÁУ¬Çó³öÊýѧÆÚÍûÖµ£®

½â´ð ½â£º£¨¢ñ£©¼ÆËã$\overline{x}$=$\frac{1}{6}$¡Á£¨1+2+3+5+6+7£©=4£¬
$\overline{y}$=$\frac{1}{6}$¡Á£¨60+55+53+46+45+41£©=50£¬
$\sum_{i=1}^{6}$£¨x_i-$\overline{x}$£©£¨y_i-$\overline{y}$£©=£¨-3£©¡Á10+£¨-2£©¡Á5+£¨-1£©¡Á3+1¡Á£¨-4£©+2¡Á£¨-5£©+3¡Á£¨-9£©=-84£¬
$\sum_{i=1}^{6}$${{£¨x}_{i}-\overline{x}£©}^{2}$=£¨-3£©²+£¨-2£©²+£¨-1£©²+1²+2²+3²=28£»
¡à»Ø¹éϵÊýΪ$\widehat{b}$=$\frac{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©£¨{y}_{i}-\overline{y}£©}{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©^{2}}$=$\frac{-84}{28}$=-3£¬
$\widehat{a}$=$\overline{y}$-$\widehat{b}$$\overline{x}$=50-£¨-3£©¡Á4=62£¬
¡à¸Ã×÷ÎïµÄÄêÊÕ»ñÁ¿y¹ØÓÚËü¡±Ïà½ü¡°×÷ÎïµÄÖêÊýxµÄÏßÐԻع鷽³ÌÊÇ$\stackrel{¡Ä}{y}$=-3x+62£»
£¨¢ò£©ÓÉ£¨¢ñ£©ÖлعéÖ±Ïß¹ý³ÌÖª£¬µ±x=2ʱ£¬$\stackrel{¡Ä}{y}$=-3¡Á2+62=56£»
µ±x=3ʱ£¬$\stackrel{¡Ä}{y}$=-3¡Á3+62=53£»
µ±x=4ʱ£¬$\stackrel{¡Ä}{y}$=-3¡Á4+62=50£»
¡àP£¨y=56£©=P£¨X=2£©=$\frac{4}{16}$=$\frac{1}{4}$£¬
P£¨Y=53£©=P£¨X=3£©=$\frac{8}{16}$=$\frac{1}{2}$£¬
P£¨Y=50£©=P£¨X=4£©=$\frac{4}{16}$=$\frac{1}{4}$£»
¡àÄêÊÕ»ñÁ¿YµÄ·Ö²¼ÁÐ

Y	56	53	50
P	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{1}{4}$

ÊýѧÆÚÍûΪEY=56¡Á$\frac{1}{4}$+53¡Á$\frac{1}{2}$+50¡Á$\frac{1}{4}$=53£®

µãÆÀ ±¾Ì⿼²éÁËÏßÐԻع鷽³ÌµÄÓ¦ÓÃÎÊÌ⣬Ҳ¿¼²éÁËÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁÐÓëÆÚÍûµÄ¼ÆËãÎÊÌ⣬ÊÇÖеµÌ⣮